Question

Two angles of a hexagon are ${120}^{o}and{160}^o$. If the remaining four angles are equal, find each equal angle.

Answer 1

Two angles of a hexagon are $\text{/}{120}^o,{160}^o$

Let remaining four angles be x, x, x and x.

Their sum $=4x+{280}^o$

But sum of all the interior angles of a hexagon

$=(6-2)\times {180}^o=4\times {180}^o={270}^o\therefore 4x+{280}^o={720}^o\Rightarrow 4x={720}^o-{280}^o={440}^o\Rightarrow x={110}^o\therefore \text{Equal angles are}{110}^o\left(each\right)$