Question

Question 125

Find the values of x and y in the given figure.

Answer 1

In $\Delta TQS$, $\angle T+\angle Q+\angle S={180}^{\circ }$ [angle sum property of a triangle]
$\Rightarrow {50}^{\circ }+{30}^{\circ }+\angle 1={180}^{\circ }\Rightarrow {80}^{\circ }+\angle 1={180}^{\circ }\Rightarrow \angle 1={180}^{\circ }-{80}^{\circ }={100}^{\circ }$
Now, $\angle 1+x={180}^{\circ }$ [linear pair]
$\Rightarrow {100}^{\circ }+x={180}^{\circ }\Rightarrow x={180}^{\circ }-{100}^{\circ }\Rightarrow x={80}^{\circ }$
In $\Delta TSR,x+{45}^{\circ }+\angle 2={180}^{\circ }$ [angle sum property of a triangle]
$\Rightarrow \angle 2={180}^{\circ }-{80}^{\circ }-{45}^{\circ }={55}^{\circ }$
Now, ${50}^{\circ }+\angle 2+y={180}^{\circ }$ [linear pair]
$\Rightarrow y={180}^{\circ }-{50}^{\circ }-{55}^{\circ }={75}^{\circ }$