Question

Question 1
If three angles of a quadrilateral are each equal to ${75}^{\circ }$, the fourth angle is
a) ${150}^{\circ }$
b) ${135}^{\circ }$
c) ${45}^{\circ }$
d) ${75}^{\circ }$

Answer 1

Given, three angles of a quadrilateral $={75}^{\circ }$
Let the fourth angle be $x^{\circ }$.
Then, according to the property, ${75}^{\circ }+{75}^{\circ }+{75}^{\circ }+x^{\circ }={360}^{\circ }$, since sum of the angles of a quadrilateral is ${360}^{\circ }$.
So, ${225}^{\circ }+x^{\circ }={360}^{\circ }$ or $x^{\circ }={360}^{\circ }–{225}^{\circ }={135}^{\circ }$
Hence, the fourth angle is ${135}^{\circ }$.