Maths4U Original · Short practice

Two parallel lines are cut by a transversal, making an acute angle \(\displaystyle \alpha =55\)°. Separately, triangle PQR has interior angles \(\displaystyle P=55\)° and \(\displaystyle Q=51\)°.

Find the angle co-interior with α, in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Two parallel lines are cut by a transversal, making an acute angle \(\displaystyle \alpha =56\)°. Separately, triangle PQR has interior angles \(\displaystyle P=56\)° and \(\displaystyle Q=52\)°.

Find the angle co-interior with α, in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Two parallel lines are cut by a transversal, making an acute angle \(\displaystyle \alpha =56\)°. Separately, triangle PQR has interior angles \(\displaystyle P=56\)° and \(\displaystyle Q=52\)°.

Find the angle corresponding to α, in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Two parallel lines are cut by a transversal, making an acute angle \(\displaystyle \alpha =57\)°. Separately, triangle PQR has interior angles \(\displaystyle P=57\)° and \(\displaystyle Q=53\)°.

Find the angle corresponding to α, in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Two parallel lines are cut by a transversal, making an acute angle \(\displaystyle \alpha =57\)°. Separately, triangle PQR has interior angles \(\displaystyle P=57\)° and \(\displaystyle Q=53\)°.

Find angle R in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Two parallel lines are cut by a transversal, making an acute angle \(\displaystyle \alpha =58\)°. Separately, triangle PQR has interior angles \(\displaystyle P=58\)° and \(\displaystyle Q=54\)°.

Find angle R in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Two parallel lines are cut by a transversal, making an acute angle \(\displaystyle \alpha =58\)°. Separately, triangle PQR has interior angles \(\displaystyle P=58\)° and \(\displaystyle Q=54\)°.

Find the exterior angle at R formed by extending QR beyond R, in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

Two parallel lines are cut by a transversal, making an acute angle \(\displaystyle \alpha =59\)°. Separately, triangle PQR has interior angles \(\displaystyle P=59\)° and \(\displaystyle Q=55\)°.

Find the exterior angle at R formed by extending QR beyond R, in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A convex regular polygon has 8 sides.

Find each exterior angle in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A convex regular polygon has 9 sides.

Find each exterior angle in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A convex regular polygon has 9 sides.

Find each interior angle in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A convex regular polygon has 10 sides.

Find each interior angle in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A convex regular polygon has 10 sides.

Find the sum of the interior angles in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A convex regular polygon has 11 sides.

Find the sum of the interior angles in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A convex regular polygon has 11 sides.

How many triangles result when diagonals from one vertex triangulate this convex polygon?

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A convex regular polygon has 12 sides.

How many triangles result when diagonals from one vertex triangulate this convex polygon?

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

AB is a diameter of a circle, \(\displaystyle AB=20 \mathrm{cm}. C\) is a different point on the circle and \(\displaystyle AC=12 \mathrm{cm}\).

Find BC in cm.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

AB is a diameter of a circle, \(\displaystyle AB=25 \mathrm{cm}. C\) is a different point on the circle and \(\displaystyle AC=15 \mathrm{cm}\).

Find BC in cm.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

AB is a diameter of a circle, \(\displaystyle AB=25 \mathrm{cm}. C\) is a different point on the circle and \(\displaystyle AC=15 \mathrm{cm}\).

Find the area of triangle ABC in \(\displaystyle \mathrm{cm}^{2}\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

AB is a diameter of a circle, \(\displaystyle AB=30 \mathrm{cm}. C\) is a different point on the circle and \(\displaystyle AC=18 \mathrm{cm}\).

Find the area of triangle ABC in \(\displaystyle \mathrm{cm}^{2}\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

AB is a diameter of a circle, \(\displaystyle AB=30 \mathrm{cm}. C\) is a different point on the circle and \(\displaystyle AC=18 \mathrm{cm}\).

Find the radius of the circle in cm.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

AB is a diameter of a circle, \(\displaystyle AB=35 \mathrm{cm}. C\) is a different point on the circle and \(\displaystyle AC=21 \mathrm{cm}\).

Find the radius of the circle in cm.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

AB is a diameter of a circle, \(\displaystyle AB=35 \mathrm{cm}. C\) is a different point on the circle and \(\displaystyle AC=21 \mathrm{cm}\).

Write the circumference as kπ cm. Find k.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

AB is a diameter of a circle, \(\displaystyle AB=5 \mathrm{cm}. C\) is a different point on the circle and \(\displaystyle AC=3 \mathrm{cm}\).

Write the circumference as kπ cm. Find k.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

AB is a chord, O is the centre, and C and D are points on the major arc AB. The angle ACB is 28°. A tangent touches at A. Separately, P,Q,R,S in this order form a cyclic quadrilateral with interior angle \(\displaystyle P=48\)°.

Find the minor angle AOB in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

AB is a chord, O is the centre, and C and D are points on the major arc AB. The angle ACB is 29°. A tangent touches at A. Separately, P,Q,R,S in this order form a cyclic quadrilateral with interior angle \(\displaystyle P=49\)°.

Find the minor angle AOB in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

AB is a chord, O is the centre, and C and D are points on the major arc AB. The angle ACB is 29°. A tangent touches at A. Separately, P,Q,R,S in this order form a cyclic quadrilateral with interior angle \(\displaystyle P=49\)°.

Find angle OAB in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

AB is a chord, O is the centre, and C and D are points on the major arc AB. The angle ACB is 30°. A tangent touches at A. Separately, P,Q,R,S in this order form a cyclic quadrilateral with interior angle \(\displaystyle P=50\)°.

Find angle OAB in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

AB is a chord, O is the centre, and C and D are points on the major arc AB. The angle ACB is 30°. A tangent touches at A. Separately, P,Q,R,S in this order form a cyclic quadrilateral with interior angle \(\displaystyle P=50\)°.

Find the acute angle between the tangent at A and chord AB, in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

AB is a chord, O is the centre, and C and D are points on the major arc AB. The angle ACB is 31°. A tangent touches at A. Separately, P,Q,R,S in this order form a cyclic quadrilateral with interior angle \(\displaystyle P=51\)°.

Find the acute angle between the tangent at A and chord AB, in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

AB is a chord, O is the centre, and C and D are points on the major arc AB. The angle ACB is 31°. A tangent touches at A. Separately, P,Q,R,S in this order form a cyclic quadrilateral with interior angle \(\displaystyle P=51\)°.

Find interior angle R of PQRS in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

AB is a chord, O is the centre, and C and D are points on the major arc AB. The angle ACB is 32°. A tangent touches at A. Separately, P,Q,R,S in this order form a cyclic quadrilateral with interior angle \(\displaystyle P=52\)°.

Find interior angle R of PQRS in degrees.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A circle has centre O and radius 30 cm. A chord AB is 18 cm from O. Separately, an external point P has \(\displaystyle OP=78 \mathrm{cm}\) and tangents PT and PU.

Find the length of AB in cm.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A circle has centre O and radius 35 cm. A chord AB is 21 cm from O. Separately, an external point P has \(\displaystyle OP=91 \mathrm{cm}\) and tangents PT and PU.

Find the length of AB in cm.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A circle has centre O and radius 35 cm. A chord AB is 21 cm from O. Separately, an external point P has \(\displaystyle OP=91 \mathrm{cm}\) and tangents PT and PU.

Find PT in cm.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A circle has centre O and radius 5 cm. A chord AB is 3 cm from O. Separately, an external point P has \(\displaystyle OP=13 \mathrm{cm}\) and tangents PT and PU.

Find PT in cm.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A circle has centre O and radius 5 cm. A chord AB is 3 cm from O. Separately, an external point P has \(\displaystyle OP=13 \mathrm{cm}\) and tangents PT and PU.

Find PU in cm.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A circle has centre O and radius 10 cm. A chord AB is 6 cm from O. Separately, an external point P has \(\displaystyle OP=26 \mathrm{cm}\) and tangents PT and PU.

Find PU in cm.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A circle has centre O and radius 10 cm. A chord AB is 6 cm from O. Separately, an external point P has \(\displaystyle OP=26 \mathrm{cm}\) and tangents PT and PU.

Find the perimeter of quadrilateral OTPU in cm.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A circle has centre O and radius 15 cm. A chord AB is 9 cm from O. Separately, an external point P has \(\displaystyle OP=39 \mathrm{cm}\) and tangents PT and PU.

Find the perimeter of quadrilateral OTPU in cm.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.