Question

Question 6
In the figure, POQ is a line. The value of x is:


A) ${20}^{\circ }$
B) ${25}^{\circ }$
C) ${30}^{\circ }$
​​​​​​​D) ${35}^{\circ }$

Answer 1

The answer is A.


POQ is a line segment.
$\therefore \angle POQ={180}^{\circ }\Rightarrow \angle POA+\angle AOB+\angle BOQ={180}^{\circ }\Rightarrow {40}^{\circ }+4x+3x={180}^{\circ }[Putting\angle POA={40}^{\circ },\angle AOB=4xand\angle BOQ=3x]\Rightarrow 7x={180}^{\circ }-{40}^{\circ }\Rightarrow 7x={140}^{\circ }\Rightarrow x=\frac{{140}^{\circ }}{7}\therefore x={20}^{\circ }$