ACT Math : How to find an angle in a rhombus

Study concepts, example questions & explanations for ACT Math

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Example Questions

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Example Question #441 : Plane Geometry

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 #442 : Plane Geometry

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 #443 : Plane Geometry

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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