Question

Question 8

In the given figure, PB = PD. The value of x is

a) ${85}^{\circ }$
b) ${90}^{\circ }$
c) ${25}^{\circ }$
d) ${35}^{\circ }$

Answer 1

In $\Delta PBD$
$\angle 1+{120}^{\circ }={180}^{\circ }$ [linear pair]
$\angle 1={180}^{\circ }-{120}^{\circ }={60}^{\circ }$
Also, $\angle 1=\angle 2={60}^{\circ }$ [$\because$ PB = PD]

Also, $\angle 2+\angle 3={180}^{\circ }$ [linear pair]
$\Rightarrow {60}^{\circ }+\angle 3={180}^{\circ }\Rightarrow \angle 3={180}^{\circ }-{60}^{\circ }\Rightarrow \angle 3={120}^{\circ }$
In $\Delta PDC,{35}^{\circ }+\angle 3+x^{\circ }={180}^{\circ }$ [angle sum property of a triangle]
$\Rightarrow {35}^{\circ }+{120}^{\circ }+x^{\circ }={180}^{\circ }\Rightarrow {155}^{\circ }+x^{\circ }={180}^{\circ }\Rightarrow x^{\circ }={180}^{\circ }-{155}^{\circ }\Rightarrow x={25}^{\circ }$