1. Find the sizes of the labelled angles. a. Given angles: 87°, 112°, 95°. Since these are labelled, no calculation needed. b. Given angles: 126°, 78°. No calculation needed. c. Given angles: 72°, 120°, 118°, 68°. No calculation needed. d. Given angles: 100°, 100°, 100°, 100°. No calculation needed. 2. Find the size of each exterior angle of a regular nonagon (9 sides) and each interior angle. - Sum of exterior angles of any polygon = 360°. - Each exterior angle = $$\frac{360}{9} = 40°$$. - Each interior angle = $$180° - 40° = 140°$$. 3. Find the size of each interior angle of a regular 12-sided figure. - Each exterior angle = $$\frac{360}{12} = 30°$$. - Each interior angle = $$180° - 30° = 150°$$. 4. Each interior angle of a regular polygon is 150°. Find the exterior angle and number of sides. - Exterior angle = $$180° - 150° = 30°$$. - Number of sides = $$\frac{360}{30} = 12$$. 5. Exterior angle = 24°. a. Number of sides = $$\frac{360}{24} = 15$$. b. Interior angle = $$180° - 24° = 156°$$. c. Sum of interior angles = $$(15 - 2) \times 180° = 13 \times 180° = 2340°$$. 6. Exterior angle = 12°. - Number of sides = $$\frac{360}{12} = 30$$. - Sum of interior angles = $$(30 - 2) \times 180° = 28 \times 180° = 5040°$$. 7. Hexagonal paving brick with angles 135° at A, F, E. a. Calculate angle x = <∠AEF. - At vertex E, angles around point sum to 360°. - Given two angles 135° and x, plus the angle adjacent to x (which is 135°), so: $$135° + x + 135° = 360°$$ $$x = 360° - 270° = 90°$$. b. Jason's bricks work because the angles fit together without gaps; the 135° angles and right angle x allow the bricks to tile the plane perfectly. 8. Regular octagon paving stones. a. Exterior angle = $$\frac{360}{8} = 45°$$. b. Interior angle = $$180° - 45° = 135°$$. c. The stones do not fit perfectly because the interior angles (135°) do not divide evenly into 360°, so gaps appear when tiling.