Question

$\text{If one angle of parallelogram is}{90}^{\circ },\text{then all the other angles are equal to}$.

• A. ${90}^{\circ }$
• B. ${180}^{\circ }$
• C. ${45}^{\circ }$

Answer 1

The correct option is A ${90}^{\circ }$

$\text{Given: One of the angles of a}\text{parallelogram is}{90}^{\circ }.$

$\text{Let ABCD be parallelogram and let}\angle Abe{90}^{\circ }.\Rightarrow \angle A+\angle B={180}^{\circ }\text{(Adjacent angles of a parallelogram}\text{are supplementary)}\Rightarrow {90}^{\circ }+\angle B={180}^{\circ }\therefore \angle B={90}^{\circ }$

$\text{Since, Opposite angles of a}\text{parallelogram are equal,}\text{then,}\angle A=\angle C\text{and}\angle B=\angle D$

$\therefore \angle A=\angle B=\angle C=\angle D={90}^{\circ }.$