Equiangular Hexagon !

Level pending

In the equiangular hexagon above, $NS = 5, SR = 3, RQ = 6, QP = 7, MP = y$ and $MN = x$ .

Find the value of $x + y$ .

1 solution

Rocco Dalto
Jul 20, 2020

$\theta = \dfrac{180 * 4}{6} = 120^{\circ}$

In the diagram above $\triangle{ABC}$ is equilateral $\implies BC = AB$ and $BC = AC$

$\implies 14 = 5 + x + y$ and $14 = 13 + y \implies 9 = x + y$ and $y = 1 \implies x = 8$

$\implies x + y = \boxed{9}$ .