How to find an angle in a rhombus - Geometry
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Given: Parallelogram 
such that 
.
True or false: Parallelogram 
cannot be a rhombus.
Given: Parallelogram
True or false: Parallelogram
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 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".
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Given: Rhombus 
with diagonals 
and 
intersecting at point 
.
True or false: 
must be a right angle.
Given: Rhombus
True or false:
One characteristic of a rhombus is that its diagonals are perpendicular. It follows that must be a right angle.
One characteristic of a rhombus is that its diagonals are perpendicular. It follows that
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Given Rhombus 
and diagonal 
.
Given Rhombus
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,
.
The rhombus referenced is below:
As a rhombus is a parallelogram, consecutive angles
Set
A diagonal of a rhombus bisects the angles at its endpoints, so, specifically,
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A rhombus has two interior angles with a measurement of 
degrees. What is the measurement of each of the other two interior angles?
A rhombus has two interior angles with a measurement of
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:
The four interior angles in any rhombus must have a sum of
Thus, if a rhombus has two interior angles of
Check:
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In the above rhombus, angle 
degrees. Find the sum of angles 
and 
In the above rhombus, 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 
, 
And 
So, 
The four interior angles in any rhombus must have a sum of
Since
And
So,
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Using the rhombus above, find the sum of angles 
and 
Using the rhombus above, find the sum of angles
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, 
The four interior angles in any rhombus must have a sum of
The opposite interior angles must be equivalent, and the adjacent angles have a sum of
Since
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In the rhombus shown above, angle 
has a measurement of 
degrees. Find the measurement of angle 
.
In the rhombus shown above, 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:
The four interior angles in any rhombus must have a sum of
The opposite interior angles must be equivalent, and the adjacent angles have a sum of
Since angle
The solution is:
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Angle 
has a measurement of 
degrees. Find the sum of angles 
and 
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, 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.
The four interior angles in any rhombus must have a sum of
The opposite interior angles must be equivalent, and the adjacent angles have a sum of
Since, both angles
Angle
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In the rhombus shown above, angle has a measurement of degrees. Find the sum of angles 
and 
In the rhombus shown above, 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.
Angles 
and 
are opposite interior angles, so they must have equivalent measurements.
The sum is:
The four interior angles in any rhombus must have a sum of
The opposite interior angles must be equivalent, and the adjacent angles have a sum of
Angles
The sum is:
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A rhombus has two interior angles with a measurement of degrees. What is the measurement of each of the other two interior angles?
A rhombus has two interior angles with a measurement of
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:
The four interior angles in any rhombus must have a sum of
Thus, if a rhombus has two interior angles of
Check:
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In the above rhombus, angle degrees. Find the sum of angles and
In the above rhombus, 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 ,
And
So,
The four interior angles in any rhombus must have a sum of
Since
And
So,
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Using the rhombus above, find the sum of angles and
Using the rhombus above, find the sum of angles
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,
The four interior angles in any rhombus must have a sum of
The opposite interior angles must be equivalent, and the adjacent angles have a sum of
Since
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In the rhombus shown above, angle has a measurement of degrees. Find the measurement of angle .
In the rhombus shown above, 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:
The four interior angles in any rhombus must have a sum of
The opposite interior angles must be equivalent, and the adjacent angles have a sum of
Since angle
The solution is:
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Angle has a measurement of degrees. Find the sum of angles and
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, 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.
The four interior angles in any rhombus must have a sum of
The opposite interior angles must be equivalent, and the adjacent angles have a sum of
Since, both angles
Angle
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In the rhombus shown above, angle has a measurement of degrees. Find the sum of angles and
In the rhombus shown above, 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.
Angles and are opposite interior angles, so they must have equivalent measurements.
The sum is:
The four interior angles in any rhombus must have a sum of
The opposite interior angles must be equivalent, and the adjacent angles have a sum of
Angles
The sum is:
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Given: Parallelogram such that .
True or false: Parallelogram cannot be a rhombus.
Given: Parallelogram
True or false: Parallelogram
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 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".
Compare your answer with the correct one above
Given: Rhombus with diagonals and intersecting at point .
True or false: must be a right angle.
Given: Rhombus
True or false:
One characteristic of a rhombus is that its diagonals are perpendicular. It follows that must be a right angle.
One characteristic of a rhombus is that its diagonals are perpendicular. It follows that
Compare your answer with the correct one above
Given Rhombus and diagonal .
Given Rhombus
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,
.
The rhombus referenced is below:
As a rhombus is a parallelogram, consecutive angles
Set
A diagonal of a rhombus bisects the angles at its endpoints, so, specifically,
Compare your answer with the correct one above
A rhombus has two interior angles with a measurement of degrees. What is the measurement of each of the other two interior angles?
A rhombus has two interior angles with a measurement of
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:
The four interior angles in any rhombus must have a sum of
Thus, if a rhombus has two interior angles of
Check:
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In the above rhombus, angle degrees. Find the sum of angles and
In the above rhombus, 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 ,
And
So,
The four interior angles in any rhombus must have a sum of
Since
And
So,
Compare your answer with the correct one above