### All Intermediate Geometry Resources

## Example Questions

### Example Question #3 : Quadrilaterals

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:**

All of the interior angles of the rhombus are degrees.

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

Both of the remaining angles are degrees.

Not enough information is provided to solve this problem.

**Correct answer:**

Both of the remaining angles are degrees.

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:

### Example Question #4 : Quadrilaterals

Using the rhombus above, find the sum of angles and

**Possible Answers:**

**Correct answer:**

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,

### Example Question #3 : Quadrilaterals

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

**Possible Answers:**

**Correct answer:**

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,

### Example Question #4 : Quadrilaterals

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

**Possible Answers:**

**Correct answer:**

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:

### Example Question #5 : Quadrilaterals

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

**Possible Answers:**

**Correct answer:**

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:

### Example Question #8 : Quadrilaterals

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

**Possible Answers:**

**Correct answer:**

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.

### Example Question #9 : Quadrilaterals

Given: Parallelogram such that .

True or false: Parallelogram cannot be a rhombus.

**Possible Answers:**

False

True

**Correct answer:**

False

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".

### Example Question #1 : Quadrilaterals

Given: Rhombus with diagonals and intersecting at point .

True or false: must be a right angle.

**Possible Answers:**

False

True

**Correct answer:**

True

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

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

Given Rhombus and diagonal .

**Possible Answers:**

**Correct answer:**

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,

.