Question

If the measures of three angles of a quadrilateral are ${100}^{\circ },{84}^{\circ }$ and ${76}^{\circ }$ then, find the measure of fourth angle.

Answer 1

Let the measure of the fourth angle be $x^{\circ }$.
The sum of the angles of a quadrilateral is ${360}^{\circ }$. So,
${100}^{\circ }+{84}^{\circ }+{76}^{\circ }+x^{\circ }={360}^{\circ }$
${260}^{\circ }+x^{\circ }={360}^{\circ }$
$x^{\circ }={100}^{\circ }$
Hence, the measure of the fourth angle is ${100}^{\circ }$.