All Intermediate Geometry Resources
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,
.