Question

If the figure "ABCD" is a parallelogram. Find the value of x and y?

• A. $x={45}^{\circ },y={50}^{\circ }$
• B. $x={55}^{\circ },y={30}^{\circ }$
• C. $x={45}^{\circ },y={30}^{\circ }$
• D. $x={55}^{\circ },y={25}^{\circ }$

Answer 1

The correct option is C $x={45}^{\circ },y={30}^{\circ }$

(Opposite angles of a parallelogram are equal)

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

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

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

(Adjacent angles of a parallelogram are supplementary)

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

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

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

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

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