Question

The angles of a quadrilateral are of the measures $120$${}^o$, $90$${}^o$, $72$${}^o$ and $x$${}^o$, then find $x$.

Answer 1

We know, by angle sum property, the sum of angles of a quadrilateral is ${360}^o$.

The given angles are ${120}^o,{90}^o,{72}^o,x$.

Then,

${120}^o+{90}^o+{72}^o+x={360}^o$.

$\Rightarrow$ $x={360}^o-({120}^o+{90}^o+{72}^o)$

$\Rightarrow$ $x={360}^o-{282}^o={78}^{\circ }$.

Therefore, the unknown angle is $x={78}^o$.