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Intermediate Geometry : 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

A rhombus has two interior angles with a measurement of degrees. What is the measurement of each of the other two interior angles?

Possible Answers:

Not enough information is provided to solve this problem.

One angle is 124 degrees and the other angle must be degrees.

Both of the remaining angles are 124 degrees.

All of the interior angles of the rhombus are degrees.

Correct answer:

Both of the remaining angles are 124 degrees.

Explanation:

The four interior angles in any rhombus must have a sum of 360 degrees. The opposite interior angles must be equivalent, and the adjacent angles have a sum of 180 degrees.

Thus, if a rhombus has two interior angles of degrees, there must also be two angles that equal:

180-56=124

Check:

56+56+124+124=360

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

Rhombus_missing_angle_dos

Using the rhombus above, find the sum of angles and

Possible Answers:

$158^\circ$

$101^\circ$

$202^\circ$

$79^\circ$

Correct answer:

$158^\circ$

Explanation:

The four interior angles in any rhombus must have a sum of 360 degrees.

The opposite interior angles must be equivalent, and the adjacent angles have a sum of 180 degrees.

Since $\measuredangle C=79^\circ$ then, $\measuredangle A=79^\circ$

$79+79=158^\circ$

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

Rhombus_missing_angle_dos

In the above rhombus, angle C=79 degrees. Find the sum of angles and

Possible Answers:

$110^\circ$

$158^\circ$

$101^\circ$

$202^\circ$

Correct answer:

$202^\circ$

Explanation:

The four interior angles in any rhombus must have a sum of 360 degrees. The opposite interior angles must be equivalent, and the adjacent angles have a sum of 180 degrees.

Since $\measuredangle C=79^\circ$ , $\measuredangle B =180-79=101^\circ$

And $\measuredangle B=\measuredangle D$

So, $101+101=202^\circ$

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Example Question #4 : How To Find An Angle In A Rhombus

Vt_vt_rhomb_tres

In the rhombus shown above, angle has a measurement of degrees. Find the measurement of angle .

Possible Answers:

$63^\circ$

$107^\circ$

$126^\circ$

$117^\circ$

Correct answer:

$117^\circ$

Explanation:

The four interior angles in any rhombus must have a sum of 360 degrees.

The opposite interior angles must be equivalent, and the adjacent angles have a sum of 180 degrees.

Since angle is adjacent to angle , they must have a sum of 180 degrees.

The solution is:

$180-63=117^\circ$

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Example Question #5 : How To Find An Angle In A Rhombus

Vt_vt_rhomb_tres

In the rhombus shown above, angle has a measurement of degrees. Find the sum of angles and

Possible Answers:

$140^\circ$

$126^\circ$

$117^\circ$

$120^\circ$

Correct answer:

$126^\circ$

Explanation:

The four interior angles in any rhombus must have a sum of 360 degrees.

The opposite interior angles must be equivalent, and the adjacent angles have a sum of 180 degrees.

Angles and are opposite interior angles, so they must have equivalent measurements.

The sum is:

$63+63=126^\circ$

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

Vt_vt_rhomb_tres

Angle has a measurement of degrees. Find the sum of angles and

Possible Answers:

$126^\circ$

$203^\circ$

$117^\circ$

$234^\circ$

Correct answer:

$234^\circ$

Explanation:

The four interior angles in any rhombus must have a sum of 360 degrees.

The opposite interior angles must be equivalent, and the adjacent angles have a sum of 180 degrees.

Since, both angles and are adjacent to angle --find the measurement of one of these two angles by: 180-63=117 .

Angle and angle must each equal 117 degrees. So the sum of angles and Y=117+117=234 degrees.

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

Given: Parallelogram ABCD such that $m \angle A = 80^{\circ }$ .

True or false: Parallelogram ABCD cannot be a rhombus.

Possible Answers:

True

False

Correct answer:

False

Explanation:

A rhombus is defined to be a parallelogram with four congruent sides; there is no restriction as to the measures of the angles. Therefore, a rhombus can have angles of any measure. The correct choice is "false".

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

Given: Rhombus ABCD with diagonals $\overline{AC}$ and $\overline{BD}$ intersecting at point .

True or false: $\angle AXB$ must be a right angle.

Possible Answers:

True

False

Correct answer:

True

Explanation:

One characteristic of a rhombus is that its diagonals are perpendicular. It follows that $\angle AXB$ must be a right angle.

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Example Question #9 : How To Find An Angle In A Rhombus

Given Rhombus ABCD and diagonal $\overline{ BD}$ .

$m \angle BCD = 124^{\circ }$

$m \angle ADB = ?$

Possible Answers:

$28^{\circ }$

$68^{\circ }$

$56^{\circ }$

$\textup{The question cannot be answered from the information given}$

$34^{\circ }$

Correct answer:

$28^{\circ }$

Explanation:

The rhombus referenced is below:

Rhombus

As a rhombus is a parallelogram, consecutive angles $\angle BCD$ and $\angle ADC$ are supplementary - that is,

$m \angle ADC + m \angle BCD = 180^{\circ }$ .

Set $m \angle BCD = 124^{\circ }$ and solve:

$m \angle ADC + 124^{\circ } = 180^{\circ }$

$m \angle ADC + 124^{\circ }- 124 ^{\circ } = 180^{\circ } - 124 ^{\circ }$

$m \angle ADC = 56 ^{\circ }$

A diagonal of a rhombus bisects the angles at its endpoints, so, specifically, $\overline{ BD}$ bisects $\angle ADC$ . Therefore,

$m \angle ADB = \frac{1}{2} m \angle ADC = \frac{1}{2} \cdot 56 ^{\circ } = 28^{\circ }$ .

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Intermediate Geometry : How to find an angle in a rhombus

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

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

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

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

Example Question #4 : How To Find An Angle In A Rhombus

Example Question #5 : How To Find An Angle In A Rhombus

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

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

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

Example Question #9 : How To Find An Angle In A Rhombus

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