Question

The adjacent angles of a parallelogram are in the ratio $4:5$, find measure of all angles of parallelogram?

Answer 1

We know that,

Sum of the adjacent angles in any parallelogram is ${180}^{\circ }$

Now,
Let first angle $=4x$ and the second angle $=5x$
$\Rightarrow 4x+5x={180}^{\circ }$
$\Rightarrow 9x={180}^{\circ }$
$\Rightarrow x=\frac{{180}^{\circ }}{9}$
$\Rightarrow x={20}^{\circ }$
Therefore, the required angles are
First angle $=4x=4\times {20}^{\circ }={80}^{\circ }$
Second angle $=5x=5\times {20}^{\circ }={100}^{\circ }$

And, we know that the opposite angles of a parallelogram are equal.

Hence, all angles of the given parallelogram are ${80}^{\circ }$, ${100}^{\circ }$, ${80}^{\circ }$ and ${100}^{\circ }$.