Question

Three angles of a hexagon are congruent. The other three angles are also congruent, each with a measure twice that of the first three. What is the measure of each angle $?$

Answer 1

Find the measure of each angle of a hexagon:

Let measure of each three congruent angle be $x°$.

Then measure of each next three congruent angles will be $2x°$.

Find the sum of all angles of hexagon:

$$\begin{gathered} =x°+x°+x°+2x°+2x°+2x° \\ =9x° \end{gathered}$$

Sum of interior angles of Polygon is $(2n-4)90°$, where $n$ is number of sides of polygon.

Hexagon has $6$ sides. Hence, sum of interior angles of hexagon is

$$\begin{gathered} =(2\times 6-4)90° \\ =720° \end{gathered}$$.

Therefore, we get:

$9x=720°$

$\therefore$ $x=80°$, $2x=160°$

Therefore, the measure of each of angle is as follows:

$\mathbf{80}\mathbf{°}\mathbf{,}\mathbf{}\mathbf{80}\mathbf{°}\mathbf{,}\mathbf{}\mathbf{80}\mathbf{°}\mathbf{}\mathbf{160}\mathbf{°}\mathbf{,}\mathbf{}\mathbf{160}\mathbf{°}\mathbf{,}\mathbf{}\mathbf{160}\mathbf{°}\mathbf{.}$