# If five angles of a heptagon have measures of 80^circ, 85^circ, 175^circ, 90^circ, 140^circ, and if the other two angles are congruent, what is the measure of each of the other two angles?

Mar 8, 2017

Measure of each of the other two angles is ${165}^{\circ}$

#### Explanation:

A heptagon has seven sides and sum of its angles is $\left(7 - 2\right) \times {180}^{\circ} = {900}^{\circ}$.

As five angles add up to ${80}^{\circ} + {85}^{\circ} + {175}^{\circ} + {90}^{\circ} + {140}^{\circ} = {570}^{\circ}$

therefore remaining two angles add up to ${900}^{\circ} - {570}^{\circ} = {330}^{\circ}$

and as the two angles are congruent

measure of each of the other two angles is ${330}^{\circ} / 2 = {165}^{\circ}$