Question

Question 3

In the given figure, PQ = PS. The value of x is

a) ${35}^{\circ }$
b) ${45}^{\circ }$
c) ${55}^{\circ }$
d) ${70}^{\circ }$

Answer 1

In $\Delta PQS$,
${110}^{\circ }+\angle 1={180}^{\circ }$
$\Rightarrow \angle 1={180}^{\circ }-{110}^{\circ }$ [linear pair of angles]
$\Rightarrow \angle 1={70}^{\circ }$

Also, $\angle 1=\angle 2={70}^{\circ }$ [$\because$ PQ = PS]
Angles opposite equal sides are equal.

As we know, the measure of any exterior angle of a triangle is equal to the sum of the measures of its two interior opposite angles
$\therefore \angle 2=x+{25}^{\circ }$
$\Rightarrow {70}^{\circ }=x+{25}^{\circ }$ [$\because \angle 2={70}^{\circ }$]
$\Rightarrow x={70}^{\circ }-{25}^{\circ }\Rightarrow x={45}^{\circ }$