Question

One angle of a quadrilateral is ${90}^{\circ }$ and all other angles are equal; find each equal angle.

Answer 1

Find each equal angle

Let each of the unknown angles of the quadrilateral be $x^{\circ }$ .
Given: One angle is ${90}^{\circ }$.
We know that sum of interior angles of quadrilateral $=360°$
$\Rightarrow x^{\circ }+x^{\circ }+x^{\circ }+{90}^{\circ }={360}^{\circ }$
$\Rightarrow 3x^{\circ }={270}^{\circ }$
$\therefore x={90}^{\circ }$

Hence, each equal angle of quadrilateral is ${90}^{\circ }$ .