All Intermediate Geometry Resources
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?
One angle is degrees and the other angle must be degrees.
Both of the remaining angles are degrees.
All of the interior angles of the rhombus are degrees.
Not enough information is provided to solve this problem.
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 #2 : How To Find An Angle In A Rhombus
Using the rhombus above, find the sum of angles and
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 : How To Find An Angle In A Rhombus
In the above rhombus, angle degrees. Find the sum of angles and
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 : How To Find An Angle In A Rhombus
In the rhombus shown above, angle has a measurement of degrees. Find the measurement of angle .
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 : How To Find An Angle In A Rhombus
In the rhombus shown above, angle has a measurement of degrees. Find the sum of angles and
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 #1 : How To Find An Angle In A Rhombus
Angle has a measurement of degrees. Find the sum of angles and
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 #1 : How To Find An Angle In A Rhombus
Given: Parallelogram such that .
True or false: Parallelogram cannot be a rhombus.
True
False
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 : How To Find An Angle In A Rhombus
Given: Rhombus with diagonals and intersecting at point .
True or false: must be a right angle.
False
True
True
One characteristic of a rhombus is that its diagonals are perpendicular. It follows that must be a right angle.
Example Question #9 : How To Find An Angle In A Rhombus
Given Rhombus and diagonal .
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,
.