1. 1
   Two parallel lines are cut by a transversal. One of the angles formed at the first intersection is 65 degrees.

   (a)

   What is the size of the corresponding angle at the second intersection?

   [1 mark]

   • A$65°$
   • B$115°$
   • C$25°$
   • D$180°$

   (b)

   What is the size of the co-interior (allied) angle on the same side of the transversal?

   [1 mark]

   • A$65°$
   • B$115°$
   • C$25°$
   • D$90°$

   (c)

   What is the size of the alternate angle on the other side of the transversal?

   [1 mark]

   • A$115°$
   • B$25°$
   • C$65°$
   • D$180°$

   Total for question 1: 3 marks

2. 2
   Triangle ABC has angle A = 50 degrees and angle B = 65 degrees.

   (a)

   Find angle C.

   [2 marks]

   (b)

   Find the size of the exterior angle of the triangle at vertex C.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A regular polygon has 9 sides (a nonagon).

   (a)

   Find the sum of the interior angles, and hence find the size of one interior angle.

   [3 marks]

   (b)

   Find the size of one exterior angle of this regular nonagon, and verify that it is consistent with your answer to part (a).

   [3 marks]

   Total for question 3: 6 marks

4. 4
   In quadrilateral PQRS, angle P = $3x$ degrees, angle Q = $(2x + 10)$ degrees, angle R = $(x + 20)$ degrees, and angle S = $(4x - 10)$ degrees.

   (a)

   Using the fact that the angles of a quadrilateral sum to 360 degrees, form an equation in $x$ and solve it.

   [4 marks]

   (b)

   Using your value of $x$, find the size of each of the four angles P, Q, R and S.

   [4 marks]

   (c)

   Determine whether PQRS could be a trapezium with side QR parallel to side PS, using the fact that co-interior (allied) angles between parallel lines sum to 180 degrees. Show your reasoning using the angles found in part (b).

   [5 marks]

   Total for question 4: 13 marks

End of questions