# Intermediate Geometry : How to find an angle in a parallelogram

## Example Questions

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### Example Question #1 : How To Find An Angle In A Parallelogram

A parallelogram contains 2 angles measuring 135 and 45.  What are the measures of the other 2 angles?

Any pair of numbers which add to 180

Explanation:

Parallelograms have angles totalling 360 degrees, but also have matching pairs of angles at the ends of diagonals.  Therefore the 2 additional angles must match the 2 given in the question.

### Example Question #2 : How To Find An Angle In A Parallelogram

Using the above rhombus, find the measurement of angle

Explanation:

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal  degrees. And, the adjacent interior angles must be supplementary angles (sum of  degrees)--i.e. angles  degrees.

Thus, the solution is:

### Example Question #1 : How To Find An Angle In A Parallelogram

Using the above rhombus, find the measurement of angle

Explanation:

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal  degrees. And, the adjacent interior angles must be supplementary angles (sum of  degrees)--i.e. angles  degrees.

Thus,

### Example Question #1 : How To Find An Angle In A Parallelogram

Using the above rhombus, find the sum of angle  and angle

Explanation:

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal  degrees. And, the adjacent interior angles must be supplementary angles (sum of  degrees).

Thus, the solution is:

### Example Question #5 : How To Find An Angle In A Parallelogram

Given that the measurement of angle  degrees, find the sum of angle  and angle

Explanation:

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal  degrees. And, the adjacent interior angles must be supplementary angles (sum of  degrees)--i.e. angles  degrees.

The solution to this problem is:

Therefore,

### Example Question #6 : How To Find An Angle In A Parallelogram

Using the above rhombus, find the measurement of angle

Explanation:

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal  degrees. And, the adjacent interior angles must be supplementary angles (sum of  degrees).

Thus, the solution is:

### Example Question #7 : How To Find An Angle In A Parallelogram

In the above rhombus, angle  has a measurement of  degrees. Find the sum of angles  and

Explanation:

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal  degrees. And, the adjacent interior angles must be supplementary angles (sum of  degrees)--i.e. angles  degrees.

The solution to this problem is:

Thus,

### Example Question #8 : How To Find An Angle In A Parallelogram

Using the parallelogram above, find the measurement of angle

Explanation:

A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal  degrees. And, the adjacent interior angles must be supplementary angles (sum of  degrees).

Since, angle  and  are supplementary the solution is:

### Example Question #9 : How To Find An Angle In A Parallelogram

Using the parallelogram above, find the sum of angles  and .

Explanation:

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal  degrees. And, the adjacent interior angles must be supplementary angles (sum of  degrees).

The first step to solving this problem is to find the measurement of angle . Since angle  is a supplementary angle to angle , angle

Since, angle  and  are opposite interior angles they must be equivalent.

Thus, the final solution is:

### Example Question #10 : How To Find An Angle In A Parallelogram

Using the parallelogram above, find the sum of angles  and