1. **Problem 5:** One angle of a quadrilateral is 135°. Work out the size of the other angles. A quadrilateral has four angles that add up to 360°. 2. **Formula:** Sum of interior angles of a quadrilateral = 360°. 3. Since one angle is 135°, the sum of the other three angles is: $$360° - 135° = 225°$$ 4. Without additional information, the other three angles could be any values that add up to 225°. --- 5. **Problem 6:** Calculate the values of a and b in the given quadrilaterals. 6. For the left part quadrilateral, the angles are 105°, 80°, 85°, and a. Sum of angles = 360°: $$105° + 80° + 85° + a = 360°$$ Simplify: $$270° + a = 360°$$ Solve for a: $$a = 360° - 270° = 90°$$ 7. For the right part quadrilateral, the angles are 85°, 70°, a, and b. Sum of angles = 360°: $$85° + 70° + a + b = 360°$$ We know from the left part that $$a = 90°$$, so: $$155° + 90° + b = 360°$$ Simplify: $$245° + b = 360°$$ Solve for b: $$b = 360° - 245° = 115°$$ --- 8. **Problem 7:** One angle of a parallelogram is 62°. Work out the size of the other angles. 9. Properties of a parallelogram: - Opposite angles are equal. - Adjacent angles are supplementary (add up to 180°). 10. Given one angle is 62°, the opposite angle is also 62°. 11. Adjacent angles to 62° are: $$180° - 62° = 118°$$ 12. Therefore, the four angles of the parallelogram are: $$62°, 118°, 62°, 118°$$