Question

Two interior angles of a convex pentagon are right angles and the other three interior angles are congruent. in degrees, what is the measure of one of the three congruent interior angles?

Answer 1

`120^(0)`

Explanation:

Given: pentagon (5 sided polygon), two interior angles =
`90^(0)` each, other three interior angles are congruent.

Sum of angles in a polygon = (n - 2) ×
`180^(0)`

where n is the number of sides of the polygon.

For a pentagon, n = 5, so that;

Sum of angles in a pentagon = (5 - 2) ×
`180^(0)`

= 3 ×
`180^(0)`

=
`540^(0)`

Sum of angles in a pentagon is
`540^(0)`.

Since two interior angles are right angle, the measure of one of its three congruent interior angles can be determined by;

`540^(0)` - (2 ×
`90^(0)`) =
`540^(0)` -
`180^(0)`

=
`360^(0)`

So that;

the measure of the interior angle =
`(360^(0) )/(3)`

=
`120^(0)`

The measure of one of its three congruent interior angles is
`120^(0)`.