Question

In pentagon $MATHS$, $\angle M \cong \angle T \cong \angle H$ and $\angle A$ is supplementary to $\angle S$. How many degrees are in the measure of $\angle H$?

Answer 1

H = 120°

Explanation:

The sum of the internal angles of a polygon with n sides is given by the formula:

S = (n-2)*180

So, for a pentagon, we have n = 5, then:

S = (5-2)*180 = 540°

So we have that:

M + A + T + H + S = 540° (eq1)

M = T = H (eq2)

A + S = 180° (eq3)

Using the second and third equation in the first one, we have:

H + H + H + 180 = 540

3H = 360

H = 120°