How many degrees in a rhombus

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A rhombus has two interior angles with a measurement of 

Possible Answers:

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

Not enough information is provided to solve this problem. 

All of the interior angles of the rhombus are  degrees.

Both of the remaining angles are  degrees.

Correct answer:

Both of the remaining angles are  degrees.

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:

Using the rhombus above, find the sum of angles  and 

Correct answer:

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  then, 

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

Correct answer:

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 ,  

And 

So, 

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

Correct answer:

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:

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

Correct answer:

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.

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

The sum is:

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

Correct answer:

Explanation:

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

Given: Parallelogram  such that .

True or false: Parallelogram  cannot be a rhombus.

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".

Explanation:

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

Given Rhombus  and diagonal . 

Correct answer:

Explanation:

The rhombus referenced is below:

As a rhombus is a parallelogram, consecutive angles  and  are supplementary - that is,

.

Set  and solve:

A diagonal of a rhombus bisects the angles at its endpoints, so, specifically,  bisects . Therefore, 

.

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