Question

Three angles of a quadrilateral are of the measure 130${}^o$, 82${}^o$, 40${}^o$. Find the measure of the fourth angle.

Answer 1

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

The given angles are, ${130}^o,{82}^o,{40}^o$.

Let the fourth angle be $x^o$.

Then, ${130}^o+{82}^o+{40}^o+x^o={360}^o$.

$\Rightarrow$ ${360}^o-({130}^o+{82}^o+{40}^o)=x^{\circ }$

$\Rightarrow$ $x^o={360}^o-{252}^o={108}^{\circ }$.

Therefore, the fourth angle is $x^o={108}^o$.