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lisov135 [29]
3 years ago
15

The measure of an exterior angle of a regular polygon is 72°. How can you find the measure of an interior angle of the polygon?

Mathematics
1 answer:
madam [21]3 years ago
4 0

Answer:

Option C) Subtract 72° from 180°

Step-by-step explanation:

We are given the following in the question:

Measure of exterior angle = 72°

Properties of exterior angles:

  • An exterior angle of a polygon is an angle at a vertex of the polygon but outside the polygon.
  • It is formed by one side and the extension of an adjacent side.
  • The interior and exterior angles are supplementary.
  • Thus, the sum of the interior angle and the exterior angle is 180 degrees.
  • All the exterior angles of a regular polygon are equal in measure.

Thus, we can write:

Let x degrees be the measure of the interior angle. Thus, we can write:

x + 72 = 180\\x  = 180-72 = 108^\circ

The measure of the interior angle is 108 degrees.

Thus, the correct answer is:

Option C) Subtract 72° from 180°

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