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A parallelogram has four angles where the opposing angles are equal and the opposing sides are parallel (hence the name parallelogram) and are of equal length. All four angles must add up to 360 degrees. Since the opposing angles are equal, any two adjacent angles must therefore add up to 180 degrees.

Since A is not equal to B, the two angles must be adjacent, so we can say:

A + B = 180 degrees

Since A is 5 times B, we can now say:

5B + B = 180 degrees

Or more simply:

6B = 180 degrees

Dividing both sides by six yields B:

B = 30 degrees

Knowing B we can now determine A:

A = 5B

A = 5 x 30

A = 150 degrees

According to the rules of parallelograms, if C is opposite A then C must be 150 degrees, otherwise C must be 30 degrees.

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Opposite angles of a parallelogram are equal, and adjacent angles are supplementary. Let one angle be θ, then the adjacent angle is 4θ + 50° → θ + 4θ + 50° = 180° → 5θ = 130° → θ = 26° → The two adjacent angles are 26° and 154°. → The angles of the parallelogram are 26°, 154°, 26°, 154°.


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