Question

if an angle of a parallelogram is two third of its adjacent angle find the angles of the parallelogram

(hint: x+2÷3x=180°)​

Answer 1

Step-by-step explanation:

Let the measure of the adjacent angle of parallelogram be x°.

$\therefore \: measure \: of \: angle = \frac{2}{3} x$

$\because \:$ Adjacent angles of a parallelogram are Supplementary.

$\therefore \: x+ \frac{2}{3} x =180\degree \\\\ </p><p>\therefore \: \frac{3x+2x}{3} =180\degree \\\\</p><p>\therefore \: \frac{5x}{3} =180\degree \\\\</p><p>\therefore \:x =180\degree \times \frac{3}{5} \\\\</p><p>\therefore \:x =36\degree \times 3\\\\</p><p>\therefore \:x =108\degree \\\\</p><p>\therefore \:\frac{2}{3} x =\frac{2}{3}\times 108\degree=72\degree </p><p>$

$\because \:$ Opposite angles of a parallelogram are congruent.

$\therefore \:$ measures of the angles of parallelogram are 72°, 108°, 72° & 108°.