Question

Question 1
Three angles of a quadrilateral are ${75}^{\circ },{90}^{\circ }and{75}^{\circ }$, then the fourth angle is
(a) ${90}^{\circ }$
(b) ${95}^{\circ }$
(c) ${105}^{\circ }$
(d) ${120}^{\circ }$

Answer 1

$\text{Given}\angle A={75}^{\circ },\angle B={90}^{\circ }\text{and}\angle {75}^{\circ }$
We know that, sum of all the angles of a quadrilateral is ${360}^{\circ }.$
$\angle A+\angle B+\angle C+\angle D={360}^{\circ }$
$\Rightarrow {75}^{\circ }+{90}^{\circ }+{75}^{\circ }+\angle D={360}^{\circ }$
$\therefore \angle D={360}^{\circ }-({75}^{\circ }+{90}^{\circ }+{75}^{\circ })$
$={360}^{\circ }-{240}^{\circ }={120}^{\circ }$
Hence, the fourth angle of a quadrilateral is ${120}^{\circ }$