Question

If an angle of a parallelogram is four fifths of its adjacent angle, find the angles of the parallelogram.

Answer 1

ANSWER:

Let ABCD be a parallelogram.
$\therefore \angle A=\angle C$ and $\angle B=\angle D$ (Opposite angles)
Let $\angle A=x^0$ and $\angle B={\frac{4x}{5}}^0$
Now, $\angle A+\angle B={180}^0$
(Adjacent angles are supplementary)
⇒$x+{\frac{4x}{5}}^0={180}^0$

⇒$\frac{9x}{5}={180}^0$

$\Rightarrow x=20\times 5$

⇒$x={100}^0$

Now, $\angle A={100}^0$ and $\angle B=\frac{4}{5}\times {100}^0={80}^0$

Hence, $\angle A=\angle C={100}^0$

$\angle B=\angle D={80}^0$