Question

Three angles of a quadrilateral are ${75}^{\circ },{90}^{\circ }$ and ${75}^{\circ }$. The measure of the fourth angle is _____________ .

Answer 1

Let the measure of the fourth angle be x.

We have,
Sum of all the angles of a quadrilateral = 360°
⇒ 75° + 90° + 75° + x = 360°
⇒ 240° + x = 360°
​⇒ x = 360° − 240°
​⇒ x = 120°


Hence, the measure of the fourth angle is 120°.