Geometry - 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 .

$117^\circ$

$63^\circ$

$107^\circ$

$126^\circ$

Explanation

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

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

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

The solution is:

$180-63=117^\circ$

Vt_vt_rhomb_tres

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

$234^\circ$

$203^\circ$

$117^\circ$

$126^\circ$

Explanation

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

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

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

Angle and angle must each equal degrees. So the sum of angles and degrees.

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

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

$m \angle ADB = ?$

$28^{\circ }$

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

$56^{\circ }$

$34^{\circ }$

$68^{\circ }$

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,

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

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

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

True

False

Explanation

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

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

True or false: Parallelogram cannot be a rhombus.

False

True

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".

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

Both of the remaining angles are degrees.

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

All of the interior angles of the rhombus are degrees.

Not enough information is provided to solve this problem.

Explanation

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

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

Check:

Rhombus_missing_angle_dos

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

$202^\circ$

$101^\circ$

$110^\circ$

$158^\circ$

Explanation

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

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