134k views
3 votes
The diagram shows a regular pentagon with centre 0. Work out the size of angle x.

2 Answers

6 votes

Explanation:

1. Use exterior angles (each adds up to 360) to find interior angles

2. Add this together

3.Take it away from 360

User Eytschkay
by
5.5k points
2 votes

Since each vertex of a pentagon has an angle measure of 108°, the size of angle x is 54°.

How to determine the size of angle x?

In Mathematics and Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:

Sum of interior angles = 180 × (n - 2)

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

Sum of interior angles = 180 × (5 - 2)

Sum of interior angles = 180 × 3

Sum of interior angles = 540°.

Measure of each interior angle = 540°/5

Measure of each interior angle = 108°

Since each vertex of a pentagon has an angle measure of 108°, we would divide the interior angle by 2;

x = 108/2

x = 54

Complete Question;

The diagram shows a regular pentagon with centre 0. Work out the size of angle x.

The diagram shows a regular pentagon with centre 0. Work out the size of angle x.-example-1
User JamesG
by
5.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.