Question

Two angles of hexagon are ${90}^0$ and ${110}^0$. If the remaining four angles are equal, find each equal angle.

Answer 1

Let us consider all the angle of hexagon as $x$

Number of sides in hexagon $n=6$

The sum of interior angle of polygon is $(2n-4)\times {90}^o$

The sum of interior angle of hexagon can be calculated as,

$(2n-4)\times {90}^o=(2\times 6-4)\times {90}^o$

$=(12-4)\times {90}^o$

$=8\times {90}^o$

We get,

$={720}^o$

The sum of interior angles of pentagon is ${720}^o$

Hence,

${90}^o+{110}^o+x+x+x+x={720}^o$

${200}^o+4x={720}^o$

$4x={720}^o-{200}^o$

$4x={520}^o$

We get,

$x={130}^o$

Hence, the measure of each equal angle $={130}^o$