Question

Question 34

The measures of $\angle x$ and $\angle y$ in the given figure are respectively.

a) ${30}^{\circ },{60}^{\circ }$
b) ${40}^{\circ },{40}^{\circ }$
c) ${70}^{\circ },{70}^{\circ }$
d) ${70}^{\circ },{60}^{\circ }$

Answer 1

As we know,
Measure of exterior angle = Sum of the opposite interior angles
$\Rightarrow \angle R\left(exterior\right)=\angle P+\angle Q$
$\Rightarrow {120}^{\circ }=x+{50}^{\circ }$ $[\because \angle R(exterior)={120}^{\circ }]$
$\Rightarrow x={120}^{\circ }-{50}^{\circ }\Rightarrow x={70}^{\circ }$
Now, the sum of the interior angles of a triangle is ${180}^{\circ }$
$\therefore x+y+{50}^{\circ }={180}^{\circ }\Rightarrow {70}^{\circ }+y+{50}^{\circ }={180}^{\circ }\Rightarrow {120}^{\circ }+y={180}^{\circ }\Rightarrow y={180}^{\circ }-{120}^{\circ }\Rightarrow y={60}^{\circ }$