Question

The sum of the angle measures of the polygon is 540°. Write and solve an equation to find the value of x.

I need the equation used to find 540 and the solution please (x=) .

Answer 1

x = 23°

Explanation:

Looking at the diagram above, we can see that it is Pentagon.

The sum of interior angles in a Pentagon (5 sides polygon) = 540°

This is because in a Pentagon, from the vertex we can draw 2 diagonals that would result in 3 triangles.

Sum of angles in a triangle = 180°

Hence, the sum of angles in a Pentagon = 3 × 180°

= 540°

Hence,

540° = 85° + 5x° + 5x° + 5x + 5° + 5x - 10°

540° = 85° + 5° - 10°+ 5x° + 5x° + 5x° + 5x°

540° = 80° + 20x°

540° - 80° = 20x°

460° = 20x°

x° = 460/20

x = 23°

Therefore, the value of x = 23°