Question

Question 13
In the given figure, POR is a line. The value of a is

(a) ${40}^{\circ }$
(b) ${45}^{\circ }$
(c) ${55}^{\circ }$
(d) ${60}^{\circ }$

Answer 1

Since POR is a line. So the sum of angle forming linear pair is ${180}^{\circ }\therefore \angle POQ+\angle ROQ={180}^{\circ }\Rightarrow (3a+5{)}^{\circ }+(2a-{25}^{\circ })={180}^{\circ }\Rightarrow 3a+5^{\circ }+2a-{25}^{\circ }={180}^{\circ }\Rightarrow 5a-{20}^{\circ }={180}^{\circ }\Rightarrow 5a={200}^{\circ }\Rightarrow a=\frac{{200}^{\circ }}{5}\Rightarrow a={40}^{\circ }$