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

Answer:

$120^{0}$

Step-by-step 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 = $\frac{360^{0} }{3}$

                                                        = $120^{0}$

The measure of one of its three congruent interior angles is $120^{0}$.