Question

THE MEASURE OF TWO ADJACENT ANGLES OF THE PARALLELOGRAM ARE IN THE RATIO OF 3:2. FIND THE MEASURE OF EACH OF THE ANGLES OF THE PARALLELOGRAM

Answer 1

Answer:

The adjacent angles are: 72 and 108

Step-by-step explanation:

Given

Angle Ratio = 3 : 2

Required

Find the measure of each angle

Let the angles be $x\ and\ y.$

Such that:

$x + y = 180$ --- adjacent angles of a parallelogram

and

$x : y = 3 : 2$ --- given

Convert to fraction

$\frac{x}{y} = \frac{3}{2}$

Cross Multiply:

$2x = 3y$

Make x the subject:

$x = \frac{3}{2}y$

$x + y = 180$ becomes

$\frac{3}{2}y + y = 180$

Take LCM

$\frac{3y + 2y}{2}= 180$

$\frac{5y}{2}= 180$

$y = \frac{2}{5} * 180$

$y = 0.4 * 180$

$y = 72$

Recall that:

$x = \frac{3}{2}y$

$x = \frac{3}{2} * 72$

$x = 1.5 * 72$

$x = 108$

Hence, the adjacent angles are: 72 and 108