Question

Adjacent angles of a parallelogram are in the ratio of 1 : 2, find the measures of all the angles of the parallelogram.

Answer 1

Let ABCD be a parallelogram in which the ratio of two adjacent angles A and B is 1 : 2
Thus, we have:
$\angle$A = x and $\angle$B = 2x


We know that the adjacent angles of a parallelogram are supplementary to each other.
Thus, we have:
$\angle$A + $\angle$B = 180°
We know:
$\angle$A = x and $\angle$B = 2x
Now,
x + 2x = 180°
$\Rightarrow$3x = 180°
$\Rightarrow$x = 60°
Thus, we get:
$\angle$A = 60° and $\angle$B = 2 × 60° = 120°
We know that opposite angles of a parallelogram are congruent.
Thus, we have:
$\angle$C = $\angle$A = 60° and $\angle$D = $\angle$B= 120°
$\therefore \mathrm{The}\mathrm{measures}\mathrm{of}\mathrm{all}\mathrm{angles}\mathrm{of}\mathrm{parallelogram}\mathrm{are}60°,120°,60°\mathrm{and}120°$