Covers Lessons 8–14: parallelograms and rectangles, special quadrilaterals (rhombus, square, kite, trapezium), the angle sum of quadrilaterals, parallel lines and transversals, angles in polygons and an introduction to congruent figures.
Question 9 3 marks
A transversal crosses two parallel lines.
(a) The co-interior angle of a 70° angle is x. Find x. 1 mark
(b) The alternate angle of a 115° angle is y. Find y. 1 mark
(c) The corresponding angle of a 48° angle is z. Find z. 1 mark
(a) Co-interior angles are supplementary: x = 180 − 70 = 110° [1]
(b) Alternate angles are equal: y = 115° [1]
(c) Corresponding angles are equal: z = 48° [1]
Question 10 3 marks
(a) Three angles of a quadrilateral are 100°, 95° and 75°. Find the fourth angle. 1 mark
In a parallelogram, one angle measures 65°.
(b) Find the size of the angle adjacent (next) to it. 1 mark
(c) Find the size of the angle opposite it. 1 mark
(a) Angle sum of a quadrilateral is 360°: 360 − 100 − 95 − 75 = 90° [1]
(b) Adjacent (co-interior) angles are supplementary: 180 − 65 = 115° [1]
(c) Opposite angles of a parallelogram are equal: 65° [1]
Question 11 4 marks
(a) Find the sum of the interior angles of an octagon (8 sides). 1 mark
(b) Hence find the size of each interior angle of a regular octagon. 2 marks
(c) Two triangles have all three pairs of corresponding sides equal. Name the congruence test that proves them congruent. 1 mark
(a) Interior angle sum = (n − 2) × 180° = (8 − 2) × 180 = 1080° [1]
(b) A regular octagon has 8 equal angles: 1080 ÷ 8 = 135° [2]
(c) SSS (side-side-side) [1]