Question

In the given figure, the value of 'x' and 'y' is:

• A. $X={45}^{\circ },Y={75}^{\circ }$
• B. $X={30}^{\circ },Y={55}^{\circ }$
• C. $X={60}^{\circ },Y={75}^{\circ }$
• D. $X={45}^{\circ },Y={30}^{\circ }$

Answer 1

The correct option is C $X={60}^{\circ },Y={75}^{\circ }$

From exterior angle property of triangles, we have
${45}^{\circ }+y={120}^{\circ }\Rightarrow y={120}^{\circ }-{45}^{\circ }={75}^{\circ }\Rightarrow y={75}^{\circ }$
From angle sum property of triangles, we have
${45}^{\circ }+{75}^{\circ }+x^{\circ }={180}^{\circ }\Rightarrow x={180}^{\circ }-{120}^{\circ }\Rightarrow x={60}^{\circ }$
Hence, the value is $x={60}^{\circ },y={75}^{\circ }$