Stage 8 - Q1 - 2 marks
Find the exterior angle x.
Hint
Choose the angle relationship or equal-distance condition that matches the givens.
Stage 8 - Q2 - 2 marks
Find the third angle of the triangle.
Hint
Choose the angle relationship or equal-distance condition that matches the givens.
Stage 8 - Q3 - 3 marks
P lies on the perpendicular bisector of AB and \(PA=5.4\) cm. Find PB and explain.
Hint
Choose the angle relationship or equal-distance condition that matches the givens.
Stage 8 - Q4 - 3 marks
A bisector creates these equal angles. Find x.
Hint
Choose the angle relationship or equal-distance condition that matches the givens.
Stage 8 - Q5 - 4 marks
Find x. Then state every possible angle size formed by this transversal and the parallel lines.
Hint
Choose the angle relationship or equal-distance condition that matches the givens.
Stage 8 - Q6 - 4 marks
Find the interior angle at B and the exterior angle x. Give a reason for each.
Hint
Choose the angle relationship or equal-distance condition that matches the givens.
Stage 8 - Q7 - 5 marks
An exterior angle \(is(4x+10)\)°. Its opposite interior angles are \((x+20)\)° and \(2x\)°. Find x and all triangle angles.
Hint
The exterior equals the sum of the opposite interior angles.
Stage 8 - Q8 - 5 marks
Points A and B are 12 cm apart. A proposed point P is 5 cm from A and 5 cm from B. Explain why no such point exists, even though the two proposed endpoint distances are equal.
Hint
Check whether the two equal-radius circles can intersect.
Stage 8 - Q9 - 5 marks
A point P lies on the perpendicular bisector of AB and angle \(PAB=42\)°. Find the other two angles of triangle APB, giving reasons.
Hint
Convert the location condition into an equal-side fact first.
Stage 8 - Q10 - 5 marks
Draw \(AB=8\) cm and a ray from A making 60° with AB. Construct a point P on the ray that is equally distant from A and B. Explain why triangle APB must be equilateral and find AP.
Hint
Combine an equal-distance construction with the given angle.