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disa [49]
2 years ago
13

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

Mathematics
2 answers:
Ivanshal [37]2 years ago
8 0

Answer:

  • 5°

Step-by-step explanation:

<h3>Solution 1</h3>

<u>Interior angle equation of the n-sided polygon:</u>

  • 180°(n - 2)

<u>Since each interior angle is 175, their sum is:</u>

  • 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.

<u>Find the measure of each exterior angle:</u>

  • 360°/72  = 5°
<h3>Solution 2</h3>

The sum of interior and exterior angles is 180.

<u>Find the value of the exterior angle:</u>

  • 180° - 175° = 5°

hammer [34]2 years ago
4 0

Answer:

  • Exterior angle = 185°

Step-by-step explanation:

<u>We know that:</u>

  • Interior angle = 175°
  • Total = 360°

<u>Solution:</u>

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

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

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