Question

$\text{What is the measure of y and x in the}\text{given figure?}$

• A. ${40}^{\circ },{80}^{\circ }$
• B. ${80}^{\circ },{50}^{\circ }$
• C. ${100}^{\circ },{40}^{\circ }$
• D. ${40}^{\circ },{100}^{\circ }$

Answer 1

The correct option is B ${80}^{\circ },{50}^{\circ }$


$\text{From the figure,}y={80}^{\circ }$
$(\because \text{Vertically opposite angles are}\text{equal})$

$\text{By angle sum property of a triangle,}x+x+y={180}^{\circ }\Rightarrow 2x+y={180}^{\circ }\Rightarrow 2x+{80}^{\circ }={180}^{\circ }\Rightarrow 2x={180}^{\circ }-{80}^{\circ }\Rightarrow 2x={100}^{\circ }\Rightarrow x={50}^{\circ }$
$\text{Hence},y={80}^{\circ }\text{and}x={50}^{\circ }.$