# Four interior angles of a pentagon measure 156°, 72°, 98°, and 87°. what is the measure of the final interior angle? 108° 127° 150° 487°?

Question: Four interior angles of a pentagon measure 156°, 72°, 98°, and 87°. what is the measure of the final interior angle? 108° 127° 150° 487°?

If you are interested in geometry, you might have encountered the problem of finding the measure of an interior angle of a polygon. In this blog post, we will show you how to solve a specific example: finding the measure of the final interior angle of a pentagon, given the measures of the other four angles.

A pentagon is a polygon with five sides and five angles. The sum of the interior angles of any pentagon is 540°, as you can find by applying the formula (n-2)×180°, where n is the number of sides. Therefore, if you know the measures of four interior angles of a pentagon, you can find the measure of the final angle by subtracting the sum of the known angles from 540°.

For example, suppose that four interior angles of a pentagon measure 156°, 72°, 98°, and 87°. What is the measure of the final interior angle? To find out, we need to add up these four angles and subtract the result from 540°:

540° - (156° + 72° + 98° + 87°) = 540° - 413° = 127°

Therefore, the measure of the final interior angle is 127°. You can check your answer by adding up all five angles and verifying that they equal 540°:

156° + 72° + 98° + 87° + 127° = 540°