Question

Find the sum of the interior angle measures of each polygon

1. 35-gon
2. 20-gon
find the measure of an exterior angle of eacch regular polygon
1. pentagon
2. 18-gon

Answer 1

The sum of the interior angles of a 35-gon is 5940°, and for a 20-gon, it is 3240°. The measure of an exterior angle for a regular pentagon is 72°, and for a regular 18-gon, it is 20°.

Step-by-step explanation:

To find the sum of the interior angle measures of a polygon, we use the formula (n - 2) × 180°, where n is the number of sides of the polygon.

1. For a 35-gon, the sum is (35 - 2) × 180° = 33 × 180° = 5940°.
2. For a 20-gon, the sum is (20 - 2) × 180° = 18 × 180° = 3240°.

The measure of an exterior angle of a regular polygon is calculated by dividing 360° by the number of sides of the polygon (since the sum of exterior angles of any polygon is 360°).

1. For a regular pentagon, the exterior angle is 360° / 5 = 72°.
2. For a regular 18-gon, the exterior angle is 360° / 18 = 20°.