Question

If the figure "ABCD" is a parallelogram. Which among the following is/are true?

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

Answer 1

Answer: (A), (C)

The correct options are
A

$x={45}^{\circ }$

C

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

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

$\Rightarrow (3x-10{)}^{\circ }$ = $(x+80{)}^{\circ }$

$\Rightarrow 2x={90}^{\circ }$

$\Rightarrow x={45}^{\circ }$

Also, adjacent angles of a parallelogram are supplementary.

$\Rightarrow (3x-10{)}^{\circ }+(y+25{)}^{\circ }={180}^{\circ }$

$\Rightarrow \left(3\right(45)-10{)}^{\circ }+(y+25{)}^{\circ }={180}^{\circ }$

$\Rightarrow (135-10{)}^{\circ }+(y+25{)}^{\circ }={180}^{\circ }$

$\Rightarrow {125}^{\circ }+y+{25}^{\circ }={180}^{\circ }$

$\Rightarrow y={180}^{\circ }–{125}^{\circ }-{25}^{\circ }$

$\Rightarrow y={180}^{\circ }–{150}^{\circ }$

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