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Ilia_Sergeevich [38]
3 years ago
8

Find the angles of a parallelogram in which an exterior angle is one-third that its interior angle.​

Mathematics
1 answer:
iogann1982 [59]3 years ago
3 0

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

x+\frac{x}{3}=180^o

solve for x

\frac{4}{3}x=180^o\\\\x=(180^o)3/4\\\\x=135^o

<em>Find the measure of the other interior angle of parallelogram</em>

Remember that consecutive interior angles are supplementary

x+y=180^o

substitute the value of x

135^o+y=180^o

solve for y

y=45^o

therefore

The angles of a parallelogram are 135°-45°-135°-45°

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