Question

If $ABCD$ is a parallelogram with two adjacent angles $A$ and $B$ equal to each other, then the parallelogram is ?

• A. Rhombus
• B. Trapezium
• C. Rectangle
• D. None of These

Answer 1

The correct option is C Rectangle

Sum of any two adjacent angles of a parallelogram is ${180}^o$.
Given, $\angle A=\angle B$
$\angle A+\angle B={180}^o$
$\Rightarrow 2\angle A={180}^o$
$\Rightarrow \angle A={90}^o$
$\Rightarrow \angle A=\angle B={90}^o$
Similarly $\angle C=\angle D={90}^o$
So, all angles are ${90}^{\circ }$ so it is a rectangle.