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

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

varsity tutors app store varsity tutors android store

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:

\(\displaystyle x=325\)

\(\displaystyle x=65\)

\(\displaystyle x=35\)

\(\displaystyle x=145\)

Correct answer:

\(\displaystyle x=145\)

Explanation:

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


\(\displaystyle \frac{360}{2}=180\)

\(\displaystyle 35+x=180\)

\(\displaystyle x=145\)

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

Rhombus

Note: Figure NOT drawn to scale.

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

Possible Answers:

\(\displaystyle x = 32\)

\(\displaystyle x = 42\)

\(\displaystyle x = 29\)

\(\displaystyle x = 58\)

\(\displaystyle x = 48\)

Correct answer:

\(\displaystyle x = 29\)

Explanation:

The diagonals of a rhombus bisect the angles.

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

Learning Tools by Varsity Tutors