Question

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?

Answer 1

Measure of each of the other two angles is `165^@`

Explanation:

A heptagon has seven sides and sum of its angles is `(7-2)xx180^@=900^@`.

As five angles add up to `80^@+85^@+175^@+90^@+140^@=570^@`

therefore remaining two angles add up to `900^@-570^@=330^@`

and as the two angles are congruent

measure of each of the other two angles is `330^@/2=165^@`