Question

A quadrilateral has three acute angles, each measuring ${65}^{\circ }$. Find the measure of fourth angle.

Answer 1

Angle of Quadrilateral –

Let us assume that ABCD is a quadrilateral --

$\begin{array}{rcl}& \Rightarrow & \angle A+\angle B+\angle C+\angle D={360}^{\circ }\\ & \Rightarrow & {65}^{\circ }+{65}^{\circ }+{65}^{\circ }+\angle D={360}^{\circ }\\ & \Rightarrow & {195}^{\circ }+\angle D={360}^{\circ }\\ & \Rightarrow & \angle D={360}^{\circ }-{195}^{\circ }\\ & \Rightarrow & \angle D={165}^{\circ }\end{array}$ ( Angle sum property of Quadrilateral. Sum of all the angles in a quadrilateral is ${360}^{\circ }$)

Therefore, the required fourth angle is ${165}^{\circ }$.