Question

Two adjacent angles of a parallelogram are in the ratio $4:5$, Find all the angles of the parallelogram

• A. $\angle C=\angle A={90}^o,\angle D=\angle B={100}^o$
• B. $\angle C=\angle A={80}^o,\angle D=\angle B={100}^o$
• C. $\angle C=\angle A=\angle D=\angle B={90}^o$
• D. None of above

Answer 1

The correct option is B $\angle C=\angle A={80}^o,\angle D=\angle B={100}^o$

Let $ABCD$ be a parallelogram.
Given that, $\angle A:\angle B=4:5$

Sum of the ratios $=4+5=9$
But, $\angle A+\angle B={180}^o$
(Adjacent angles of the parallelogram, $ABCD$)
$\therefore \angle A=\frac{4}{9}\times {180}^o={80}^o$
$\angle B=\frac{5}{9}\times {180}^o={100}^o$
So $\angle C=\angle A={80}^o,\angle D=\angle B={100}^o$
(Opposite angles of a parallelogram are equal).