Question

The adjacent angles of a parallelogram are as 2 : 3. Find the measures of all the angles

• A. ${108}^o$
• B. ${60}^o$
• C. ${116}^o$
• D. ${90}^o$

Answer 1

Answer: (A)

${108}^o$

Let ABCD be a parallelogram. Let $\angle A$ and $\angle B$ be its two adjacent angles such that $\angle A:\angle B=2:3$
Let $\angle A=2x^o$ and $\angle B=3x^o$
Since adjacent interior angles are supplementary.
$\therefore \angle A+\angle B={180}^o$
$\Rightarrow 2x^o+3x^o={180}^o$
$\Rightarrow 5x^o={180}^o\Rightarrow x^o=\frac{180}{5}={36}^o$
$\therefore \angle A=2x^o={72}^o,\angle B=3x^o={108}^o$
Since opposite angles of parallelogram are equal.
$\therefore \angle C=\angle A={72}^o$ and $\angle D=\angle B={108}^o$