Exam-Style Problems

Stage 9 - Q1 - 2 marks

19327

Find angle \(ABC\). Use the exterior angle and give a reason.

\[\angle BAC=26^\circ,\quad\angle ACD=65^\circ\]

A

B

C

D

Hint

Combine the straight-line and triangle-angle sums.

Stage 9 - Q2 - 2 marks

19328

\(AB=AC\). Find the two base angles.

\[\angle BAC=78^\circ\]

A

B

C

Hint

Subtract the vertex angle, then divide by two.

Stage 9 - Q3 - 3 marks

19329

\(AB\) is parallel to \(CD\). Find angles PQD and CQP.

\[\angle FPB=57^\circ\]

A

B

C

D

P

Q

F

E

Hint

Use the parallel lines first, then the straight line.

Stage 9 - Q4 - 3 marks

19330

ABCD is a parallelogram. Find angles \(ABC\) and ACB.

\[\angle BAC=35^\circ,\quad\angle CAD=31^\circ\]

A

B

C

D

Hint

The diagonal splits the corner at A.

Stage 9 - Q5 - 4 marks

19331

\(AB=AC=AD\). Find angles \(BAD\) and \(BCD\).

\[\angle ABC=58^\circ,\quad\angle CDA=55^\circ\]

A

B

C

D

Hint

\(AC\) is an equal side in both triangles.

Stage 9 - Q6 - 4 marks

19332

\(AB=AC=AD\). Find angles \(BAD\) and \(BCD\).

\[\angle ABC=60^\circ,\quad\angle CDA=56^\circ\]

A

B

C

D

Hint

\(AC\) is an equal side in both triangles.

Stage 9 - Q7 - 5 marks

19333

The four corner angles follow this pattern. Find \(x\) and the largest angle.

\[A=x^\circ,\ B=(x+26)^\circ\]

\[C=(x+52)^\circ,\ D=(x+78)^\circ\]

A

B

C

D

Hint

Add all four angle expressions.

Stage 9 - Q8 - 5 marks

19334

O is the centre; \(AC\) is a diameter. Find angles OAB, OCB and \(ABC\) using equal radii.

\[\angle AOB=98^\circ\]

A

C

B

O

Hint

Find both isosceles base angles before combining them.

Stage 9 - Q9 - 5 marks

19335

ABCD is a parallelogram. Find \(x\), angle DAB and angle \(ABC\).

\[\angle DAB=(2x+20)^\circ\]

\[\angle ABC=(3x+65)^\circ\]

A

B

C

D

Hint

Use the adjacent-angle relationship to construct an equation.

Stage 9 - Q10 - 3 marks

19336

\(AB=AC=AD\). The given angles are algebraic and angle \(BAD\) is \(132^\circ\). Find \(x\) and angle \(BCD\).

\[\angle ABC=(x+12)^\circ\]

\[\angle CDA=(2x+9)^\circ\]

A

B

C

D

Hint

The angles at C match the base angles at B and D.