1. GCSE Mathematics Problem Solving Shape and Measure Higher Tier

2. An interior angle of a regular polygon is four times the size of an exterior angle. What is the name of the polygon? Interior angle = Exterior angle4 x (n-2) x 180˚ n 360˚ n =4 x Solve the equation to find n (the number of sides) n(n-2) x 180 = 4n(360) n n Multiply both sides by n (n-2)180 = 4(360) 180n - 360 = 1440 Expand the brackets Add 360 to both sides What information is given in the question?

3. If n = 10 what is the name of the polygon? 180n = 1440 + 360 180n = 1800 Divide both sides by 180 n = 10 If n = 10 then the number of sides of the polygon is 10. Therefore, the polygon must be a DECAGON.