How to find an angle in a rhombus

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ISEE Upper Level Quantitative Reasoning › How to find an angle in a rhombus

Questions 1 - 2

1

Consider the rhombus below. Solve for .

Problem_10

Explanation

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

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

2

Rhombus

Note: Figure NOT drawn to scale.

The above depicts a rhombus and one of its diagonals. What is ?

Explanation

The diagonals of a rhombus bisect the angles.

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

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