Question
The measure of an exterior angle of a regular polygon is given below. Find the measure of an interior angle. Then find the number of sides. 40 What is the measure of an interior angle?
Ask by Martinez Deleon. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The measure of an interior angle is 140 degrees.
Solution
In a regular polygon, each exterior angle and its corresponding interior angle are supplementary, meaning they add up to 180 degrees.
Given:
- **Measure of an exterior angle** = 40°
To find the **measure of the interior angle**:
\[
\text{Interior Angle} = 180° - \text{Exterior Angle} = 180° - 40° = 140°
\]
**Answer:** The measure of an interior angle is 140 degrees.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To find the measure of an interior angle of a regular polygon when given the measure of an exterior angle, you can use the formula: Interior Angle = 180° - Exterior Angle. So for an exterior angle of 40°, the interior angle would be 180° - 40° = 140°. Now, to find the number of sides of the polygon, you can use the fact that the sum of all exterior angles of any polygon is always 360°. You divide 360° by the measure of the exterior angle: 360° ÷ 40° = 9. Therefore, the polygon has 9 sides, meaning it is a nonagon!
