Angles in Pentagon Solved Examples
Example 1: The angles at 4 vertices of a pentagon measure 90°, 120°, 50°, and 70°. What is the measure of the remaining angle?
Solution:
We know that for a pentagon, the sum of all the interior angles equals 540°
Therefore, 90° + 120° + 50° + 70° + x = 540°
x = 540°−330°
x = 210°
Example 2: Three angles of a pentagon are 80°, 70° and 100°, then the other two angles can be 145° and 145° or 120° and 180°?
Solution:
Sum of three angles = 80° + 70° + 100° = 250°
We know that the sum of all the five angles of a pentagon is 540°.
Sum of the other two angles = 540° – 250° = 290°
Now,
145° + 145° = 290°
120° + 180° = 300°
Hence, the other two angles of a pentagon are 145° and 145°.
Example 3: If an interior angle of a regular pentagon is 9x. Then, what is the value of x?
Solution:
Each interior angle of a regular pentagon is 108°
Hence, 9 x = 108°
x = 12
Angles in a Pentagon
Pentagon is a two-dimensional (2D) five-sided polygon having five angles. In a regular pentagon, the sum of all interior angles is equal to 540° with each interior angle measuring 108°, and each exterior angle measuring 72°.
In this article, we will discuss about what is a pentagon, different types of Pentagon, various angles in the Pentagon along with some solved questions.
Table of Content
- What is a Pentagon?
- Types of Pentagon
- Angles in Pentagon
- Sum of Angles in a Pentagon
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