Question

One interior angle of a regular polygon is 175 degrees. What is the measure of one exterior angle? Step by step (please answer)

Answer 1

Answer:

• 5°

Step-by-step explanation:

Solution 1

Interior angle equation of the n-sided polygon:

• 180°(n - 2)

Since each interior angle is 175, their sum is:

• 180°(n - 2) = 175°n
• 180n - 360 = 175n
• 5n = 360
• n = 72

The polygon has 72 sides.

We know the sum of exterior angles of a polygon is 360.

Find the measure of each exterior angle:

• 360°/72  = 5°

Solution 2

The sum of interior and exterior angles is 180.

Find the value of the exterior angle:

• 180° - 175° = 5°

Answer 2

Answer:

• Exterior angle = 185°

Step-by-step explanation:

We know that:

• Interior angle = 175°
• Total = 360°

Solution:

• Exterior angle = 360 - 175
• => Exterior angle = 185°

Hence, the measure of an exterior angle is 185°.