1. 1
   A road planner is measuring angles at a junction where three straight roads meet at a single point.

   (a)

   Three roads meet at a single junction point. Two of the angles between them measure $110°$ and $140°$. Find the third angle at the junction.

   [1 mark]

   • A$110°$
   • B$140°$
   • C$130°$
   • D$100°$

   (b)

   On one of the roads, a lamppost stands where the road is straight. The angle on one side of the lamppost is $65°$. Find the angle on the other side.

   [1 mark]

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

   (c)

   Two of the roads cross, forming an X shape. One angle formed is $72°$. Find the angle vertically opposite it.

   [1 mark]

   • A$18°$
   • B$108°$
   • C$72°$
   • D$36°$

   Total for question 1: 3 marks

2. 2
   A carpenter is fitting triangular and quadrilateral fence panels and needs to check the interior angles add up correctly.

   (a)

   A fence panel is triangular, with two known interior angles of $58°$ and $74°$. Find the third angle, giving a geometric reason.

   [2 marks]

   (b)

   A quadrilateral fence panel has three known interior angles of $95°$, $80°$ and $110°$. Find the fourth angle, giving a geometric reason.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Two railway tracks run parallel to each other, crossed by a single straight sleeper acting as a transversal.

   (a)

   One angle formed between the transversal and the first track is $63°$. The corresponding angle on the second track is labelled $x$. Find $x$, giving a geometric reason.

   [3 marks]

   (b)

   The $63°$ angle lies between the two tracks. A second angle, $y$, is formed where the sleeper meets the second track, on the same side of the sleeper as the $63°$ angle and also between the two tracks, so that $y$ and the $63°$ angle are co-interior angles. Find $y$, giving a geometric reason.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   An architect is designing a gazebo with a regular polygon base and needs to calculate related angle properties for the roof structure.

   (a)

   A regular polygon is used as the base of a decorative garden gazebo. The polygon has 9 sides. Calculate the sum of its interior angles, and hence find the size of one interior angle.

   [4 marks]

   (b)

   Find the size of one exterior angle of the same 9-sided regular polygon, and use it to verify your answer to part (a) using the relationship between interior and exterior angles.

   [4 marks]

   (c)

   An irregular polygon has interior angles $x$, $x+10°$, $x+20°$, $x+30°$ and $x+40°$ (5 angles in total). Form and solve an equation to find $x$, and hence state the largest interior angle.

   [5 marks]

   Total for question 4: 13 marks

End of questions