Question

Find the number of sides of the regular polygon whose each exterior angle is
12°
Find the sum of the interior angles of a polygon with
a) 10 sides
b) 14 sides
c) 32 sides
d) 17 sides​

Answer 1

Answer:

1. Total measure of all exterior angle

= 360°

Measure of each exterior angle = 12°

Therefore, the number of sides of exterior angle of regular polygon

= 360°/n = 360°/12° = 30

So, the polygon has 30

2. a) The sum of interior angle=(n-2)×180°

= (10 - 2 ) × 180°

= 8 × 180°

= 1440°

b) The sum of interior angle = (n-2) × 180

= ( 14 - 2 ) × 180°

= 12 × 180° = 2160°

c) The sum of interior angle = ( n-2) × 180°

= ( 32-2) × 180°

= 30×180° = 5400°

d) The sum of interior angle = ( n-2) × 180°

= ( 17-2) × 180°

= 15×180° = 2700°