Answer:
The angles of a parallelogram are 135°-45°-135°-45°
Step-by-step explanation:
we know that
In a parallelogram opposites angles are congruent and consecutive angles are supplementary
Remember that
The sum of a exterior angle and its interior angle is equal to 180 degrees
Let
x ----> the measure of one interior angle of parallelogram
y ----> the measure of the other interior angle of parallelogram
we have that
[tex]x+\frac{x}{3}=180^o[/tex]
solve for x
[tex]\frac{4}{3}x=180^o\\\\x=(180^o)3/4\\\\x=135^o[/tex]
Find the measure of the other interior angle of parallelogram
Remember that consecutive interior angles are supplementary
[tex]x+y=180^o[/tex]
substitute the value of x
[tex]135^o+y=180^o[/tex]
solve for y
[tex]y=45^o[/tex]
therefore
The angles of a parallelogram are 135°-45°-135°-45°
