Question

Find the value of £ and 31.

3r
45°
45°
11
135⁹
3x°
135⁰
to

Answer 1

Based on the polygon shown in the image above, the value of x and 3x include the following;

x = 90°.

3x = 270°.

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 hexagon and it has six (6) sides.

By substituting the number of sides into the formula, we have;

Sum of interior angles = 180 × (6 - 2)

Sum of interior angles = 180 × 4

Sum of interior angles = 720°.

For the value of x, we have;

45 + 135 + 45 + 135 + 3x + x = 720°.

360 + 4x = 720°.

x = 360/4

x = 90°.

3x = 3(90)

3x = 270°.