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ISEE Upper Level Math : How to find an angle in a rhombus

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Example Questions

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

Consider the rhombus below. Solve for $\displaystyle x$ .

Problem_10

Possible Answers:

x=35 $\displaystyle x=35$

x=65 $\displaystyle x=65$

x=145 $\displaystyle x=145$

x=325 $\displaystyle x=325$

Correct answer:

x=145 $\displaystyle x=145$

Explanation:

The total sum of the interior angles of a quadrilateral is 360 $\displaystyle 360$ degrees. In this problem, we are only considering half of the interior angles:

$\frac{360}{2}=180$ $\displaystyle \frac{360}{2}=180$

$\displaystyle 35+x=180$

x=145 $\displaystyle x=145$

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Example Question #291 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Rhombus

Note: Figure NOT drawn to scale.

The above depicts a rhombus and one of its diagonals. What is $\displaystyle x$ ?

Possible Answers:

x = 32 $\displaystyle x = 32$

x = 42 $\displaystyle x = 42$

x = 48 $\displaystyle x = 48$

x = 29 $\displaystyle x = 29$

x = 58 $\displaystyle x = 58$

Correct answer:

x = 29 $\displaystyle x = 29$

Explanation:

The diagonals of a rhombus bisect the angles.

The angle bisected must be supplementary to the $122^{\circ }$ $\displaystyle 122^{\circ }$ angle since they are consecutive angles of a parallelogram; therefore, that angle has measure $\left (180 - 122 \right ) ^{\circ } = 58^{\circ }$ $\displaystyle \left (180 - 122 \right ) ^{\circ } = 58^{\circ }$ , and $\displaystyle x$ is half that, or $29^{\circ }$ $\displaystyle 29^{\circ }$ .

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ISEE Upper Level Math : How to find an angle in a rhombus

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

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

Example Question #291 : Isee Upper Level (Grades 9 12) Mathematics Achievement

All ISEE Upper Level Math Resources

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