# ACT Math : Rhombuses

## Example Questions

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

The two acute angles in a rhombus add up to . What is the measure of one of the obtuse angles in the rhombus?

Explanation:

The key here is to know that a rhombus has two pairs of congruent angles. In other words, the two acute angles of a rhombus are equal and the two obtuse angles are equal.

In this problem, since the two acute angles add up to  and they must both be the same amount, each of the acute angles must be .

It is also important to know that the four angles of a rhombus add up to . If the two acute angles add up to , then that means that the two obtuse angles must add up to , or .

Finally, because the obtuse angles add up to  and they must be congruent, each of the obtuse angles must be .

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

A rhombus has two interior angles each with a measurement of . Find the measurement for one of the two remaining angles.

Explanation:

First, consider that the sum total of the four interior angles in any rhombus must equal . Furthermore, a rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of

One way to approach this problem is to realize that each of the remaining two angles must have the same measurement, and that each will be supplementary angles with .  Find the difference between  and  to find the solution.

The correct answer is:

### Example Question #3 : How To Find An Angle In A Rhombus

A rhombus has an interior angle with a measurement of . Find the measurement for one of the angles that are adjacent to the angle that has a measurement of .

Explanation:

A rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of .

If a rhombus has an interior angle that has a measurement of , the adjacent angle must equal:

### Example Question #4 : How To Find An Angle In A Rhombus

A rhombus has two opposite interior angles that have a sum of . Find the sum of the remaining two angles.

Explanation:

The sum total of the four interior angles in any rhombus must equal . Furthermore, a rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of .

Since, two of the opposite interior angles in this rhombus have a sum measurement of , the sum of the remaining two angles must equal:

(meaning the sum of the four interior angles equals ).

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

Using the rhombus shown above, find the measurement for angle

Explanation:

A rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of .

Since this problem involves supplementary angles, the solution is:

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

A rhombus has two interior angles each with a measurement of . Find the measurement for one of the two remaining angles.

Explanation:

The sum total of the four interior angles in any rhombus must equal . Furthermore, a rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of

One way to approach this problem is to realize that each of the remaining two angles must have the same measurement, and that each will be supplementary angles with .

Find the difference between  and  to find the solution.

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

A rhombus has two interior angles each with a measurement of . Find the sum of the remaining two angles.

Explanation:

To solve this problem, consider that the sum total of the four interior angles in any rhombus must equal . Furthermore, a rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of

Since this problem provides the measurement for two of the interior angles, find the sum of those two angles. Then subtract that sum from  to find the sum of the two remaining interior angles.

The solution is:

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

A rhombus has two interior angles each with a measurement of . Find the sum of the remaining two angles.

Explanation:

To solve this problem, consider that the sum total of the four interior angles in any rhombus must equal . Furthermore, a rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of

Since this problem provides the measurement for two of the interior angles, find the sum of those two angles. Then subtract that sum from  to find the sum of the two remaining interior angles.

The solution is:

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

A rhombus has an interior angle with a measurement of . Find the measurement for one of the angles that are adjacent to the angle that has a measurement of

Explanation:

A rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of .

Therefore, if a rhombus has an interior angle that has a measurement of , then the adjacent angle must equal:

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

Using the rhombus shown above, find the measurement for angle