Question

$\text{In the given figure, ABCD is a}\text{parallelogram. From the given options,}\text{select the values of x and y.}$

• A. $x={45}^{\circ }$
• B. $y={105}^{\circ }$
• C. $y={30}^{\circ }$
• D. $x={75}^{\circ }$

Answer 1

Answer: (A), (C)

$y={30}^{\circ }$

We know that the opposite angles of a parallelogram are equal.

So,
$(3x-10{)}^{\circ }=(x+80{)}^{\circ }\Rightarrow 3x-x={80}^{\circ }+{10}^{\circ }\Rightarrow 2x={90}^{\circ }\Rightarrow x={45}^{\circ }$

Also, the consecutive angles of a parallelogram are supplementary.

So,
$\angle B+\angle C={180}^{\circ }(3x-10{)}^{\circ }+(y+25{)}^{\circ }={180}^{\circ }(3\times {45}^{\circ })-{10}^{\circ }+y+{25}^{\circ }={180}^{\circ }{135}^{\circ }-{10}^{\circ }+y+{25}^{\circ }={180}^{\circ }\Rightarrow {125}^{\circ }+y+{25}^{\circ }={180}^{\circ }\Rightarrow y={180}^{\circ }–{125}^{\circ }-{25}^{\circ }\Rightarrow y={30}^{\circ }$