Question

Two adjacent angles of a parallelogram are in the ratio of 2:3, find all the angles of the parallelogram.

Answer 1

Let $\square$ABCD be a parallelogram in which the ratio of two adjacent angles A and B is 2 : 3
Also, let $\angle$A = 2x and $\angle$B = 3x, where x is the multiple of the ratios of $\angle$A and $\angle$B.
We know that the adjacent angles of a parallelogram are supplementary.
Thus, we have:
$\angle$A + $\angle$B = 180°
We know:
$\angle$A = 2x and $\angle$B = 3x
Thus, we have:
2x + 3x = 180°
$\Rightarrow$5x = 180°
$\Rightarrow$x = 36°
Now,
$\angle$A = 2x
= 2 × 36°
= 72°
and $\angle$B = 3x
= 3 × 36°
= 108°
We know that the opposite angles of a parallelogram are congruent.
Thus, we have:
$\angle$C = $\angle$A = 72° and $\angle$D = $\angle$B = 108°
Thus, the measures of all angles of parallelogram are 72°,108°, 72° and 108°