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 [tex]x\ and\ y.[/tex]
Such that:
[tex]x + y = 180[/tex] --- adjacent angles of a parallelogram
and
[tex]x : y = 3 : 2[/tex] --- given
Convert to fraction
[tex]\frac{x}{y} = \frac{3}{2}[/tex]
Cross Multiply:
[tex]2x = 3y[/tex]
Make x the subject:
[tex]x = \frac{3}{2}y[/tex]
[tex]x + y = 180[/tex] becomes
[tex]\frac{3}{2}y + y = 180[/tex]
Take LCM
[tex]\frac{3y + 2y}{2}= 180[/tex]
[tex]\frac{5y}{2}= 180[/tex]
[tex]y = \frac{2}{5} * 180[/tex]
[tex]y = 0.4 * 180[/tex]
[tex]y = 72[/tex]
Recall that:
[tex]x = \frac{3}{2}y[/tex]
[tex]x = \frac{3}{2} * 72[/tex]
[tex]x = 1.5 * 72[/tex]
[tex]x = 108[/tex]
Hence, the adjacent angles are: 72 and 108
