ACT Math : Quadrilaterals

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : Rhombuses

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

Possible Answers:

 

Correct answer:

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:



To check your answer note: 

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

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

Act rhombus vt

Using the rhombus shown above, find the measurement for angle 

Possible Answers:

Correct answer:

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 #1 : 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. 

Possible Answers:

Correct answer:

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 #2 : Rhombuses

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

Possible Answers:

Correct answer:

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 #3 : Rhombuses

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

Possible Answers:

Correct answer:

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 #6 : 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 

Possible Answers:

Correct answer:

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 #4 : Rhombuses

Act rhombus vt

Using the rhombus shown above, find the measurement for angle 

Possible Answers:

Correct answer:

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: 



Check answer by:

Example Question #11 : Rhombuses

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

Possible Answers:

Correct answer:

Explanation:

First, consider that the sum total of the four interior angles in any rhombus must equal . Secondly, 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 . Therefore, find the difference between  and  to find the solution. 

Example Question #201 : Quadrilaterals

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

Possible Answers:

Correct answer:

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 . 

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 #13 : 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. 

Possible Answers:

Correct answer:

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:





Note: this means that each of the two remaining angles must have a measurement of .  

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