Answer:
The measure of an acute angle of the parallelogram is [tex]60^{\circ}[/tex].
Step-by-step explanation:
As we know by the property of parallelogram :
Consecutive angles of a parallelogram are supplementary.
Given: The measure of two consecutive angles of a parallelogram are in the ratio 6: 3.
Then;
6x be the measure of larger angle and 3x be the measure of smaller angle.
⇒ [tex]6x + 3x =180^{\circ}[/tex]
Combine like terms;
[tex]9x =180^{\circ}[/tex]
Divide both sides by 9 we get;
[tex]\frac{9x}{9} =\frac{180}{9}[/tex]
Simplify:
[tex]x = 20^{\circ}[/tex]
Then, the measure of larger angle 6x = [tex]6 \times 20 = 120^{\circ}[/tex] and
the measure of smaller angle 3x = [tex]3 \times 20^{\circ}=60^{\circ}[/tex].
Since, we know that in a parallelogram, opposite interior angles are equal.
Acute angle is an angle smaller than a right angle(i.e 90 degree)
Therefore, the measure of an acute angle of the parallelogram is [tex]60^{\circ}[/tex].
