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

The adjacent angles are: 72 and 108

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

`(x)/(y) = (3)/(2)`

Cross Multiply:

`2x = 3y`

Make x the subject:

`x = (3)/(2)y`

`x + y = 180` becomes

`(3)/(2)y + y = 180`

Take LCM

`(3y + 2y)/(2)= 180`

`(5y)/(2)= 180`

`y = (2)/(5) * 180`

`y = 0.4 * 180`

`y = 72`

Recall that:

`x = (3)/(2)y`

`x = (3)/(2) * 72`

`x = 1.5 * 72`

`x = 108`

Hence, the adjacent angles are: 72 and 108