Question

In a trapezium ABCD, side AB is parallel to side DC. If $\angle A=x^{\circ }$ and $\angle D=(3x-20{)}^{\circ }$, value of $x=?$

• A. $x={60}^{\circ }$
• B. $x={80}^{\circ }$
• C. $x={20}^{\circ }$
• D. $x={50}^{\circ }$

Answer 1

The correct option is D

$x={50}^{\circ }$

$\angle A=x^{\circ }$ and $\angle D=(3x-20{)}^{\circ }$

$\angle A+\angle D={180}^{\circ }$ (Co-interior angles)

$\Rightarrow x^{\circ }+(3x-20{)}^{\circ }={180}^{\circ }$

$\Rightarrow 4x-{20}^{\circ }={180}^{\circ }$

$\Rightarrow 4x={180}^{\circ }+{20}^{\circ }$

$\Rightarrow 4x={200}^{\circ }$

$\Rightarrow x={50}^{\circ }$