How to find an angle in a parallelogram - Geometry
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A parallelogram contains 2 angles measuring 135 and 45. What are the measures of the other 2 angles?
A parallelogram contains 2 angles measuring 135 and 45. What are the measures of the other 2 angles?
Parallelograms have angles totalling 360 degrees, but also have matching pairs of angles at the ends of diagonals. Therefore the 2 additional angles must match the 2 given in the question.
Parallelograms have angles totalling 360 degrees, but also have matching pairs of angles at the ends of diagonals. Therefore the 2 additional angles must match the 2 given in the question.
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Using the above rhombus, find the measurement of angle 
Using the above rhombus, find the measurement of angle
A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal
degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees)--i.e. angles
degrees.
Thus, the solution is:


A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees)--i.e. angles
degrees.
Thus, the solution is:
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Using the above rhombus, find the measurement of angle
.
Using the above rhombus, find the measurement of angle .
A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal
degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees)--i.e. angles
degrees.
Thus, 

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees)--i.e. angles
degrees.
Thus,
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Using the above rhombus, find the measurement of angle 
Using the above rhombus, find the measurement of angle
A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal
degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees).
Thus, the solution is:



A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees).
Thus, the solution is:
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Using the above rhombus, find the sum of angle
and angle
.
Using the above rhombus, find the sum of angle and angle
.
A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal
degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees).
Thus, the solution is:



A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees).
Thus, the solution is:
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Given that the measurement of angle
degrees, find the sum of angle
and angle 
Given that the measurement of angle degrees, find the sum of angle
and angle
A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal
degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees)--i.e. angles
degrees.
The solution to this problem is:




Therefore,

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees)--i.e. angles
degrees.
The solution to this problem is:
Therefore,
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In the above rhombus, angle
has a measurement of
degrees. Find the sum of angles
and 
In the above rhombus, angle has a measurement of
degrees. Find the sum of angles
and
A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal
degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees)--i.e. angles
degrees.
The solution to this problem is:




Thus,

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees)--i.e. angles
degrees.
The solution to this problem is:
Thus,
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Using the parallelogram above, find the measurement of angle 
Using the parallelogram above, find the measurement of angle
A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal
degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees).
Since, angle
and
are supplementary the solution is:

A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees).
Since, angle and
are supplementary the solution is:
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Using the parallelogram above, find the sum of angles
and
.
Using the parallelogram above, find the sum of angles and
.
A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal
degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees).
The first step to solving this problem is to find the measurement of angle
. Since angle
is a supplementary angle to angle
, angle 

Since, angle
and
are opposite interior angles they must be equivalent.
Thus, the final solution is:

A rhombus must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees).
The first step to solving this problem is to find the measurement of angle . Since angle
is a supplementary angle to angle
, angle
Since, angle and
are opposite interior angles they must be equivalent.
Thus, the final solution is:
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Using the parallelogram above, find the sum of angles
and
.
Using the parallelogram above, find the sum of angles and
.
A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal
degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees).
Since, angles
and
are opposite interior angles, they must be equivalent.
Therefore, the solution is:

A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees).
Since, angles and
are opposite interior angles, they must be equivalent.
Therefore, the solution is:
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In the parallelogram shown above, angle
is
degrees. Find the measure of angle 
In the parallelogram shown above, angle is
degrees. Find the measure of angle
A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal
degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees).
Since, angles
and
are opposite interior angles, thus they must be equivalent.
, therefore 
A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees).
Since, angles and
are opposite interior angles, thus they must be equivalent.
, therefore
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In the parallelogram shown above, angle
is
degrees. Find the sum of angles
and
.
In the parallelogram shown above, angle is
degrees. Find the sum of angles
and
.
A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal
degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees).
Thus, the solution is:

Since both angles
and
equal
There sum must equal 
A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees. And, the adjacent interior angles must be supplementary angles (sum of
degrees).
Thus, the solution is:
Since both angles and
equal
There sum must equal
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Using the parallelogram above, find the sum of angles
and 
Using the parallelogram above, find the sum of angles and
A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal
degrees.
Also, the adjacent interior angles must be supplementary angles (sum of
degrees).
Since, angles
and
are adjacent to each other they must be supplementary angles.
Thus, the sum of these two angles must equal
degrees.
A parallelogram must have equivalent opposite interior angles. Additionally, the sum of all four interior angles must equal degrees.
Also, the adjacent interior angles must be supplementary angles (sum of degrees).
Since, angles and
are adjacent to each other they must be supplementary angles.
Thus, the sum of these two angles must equal degrees.
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A paralellogram as two angles that are 65 degrees and 115 degrees respectively. What are the other two angles in the paralellogram?
A paralellogram as two angles that are 65 degrees and 115 degrees respectively. What are the other two angles in the paralellogram?
This question is very simple to answer if you remember that ALL paralellograms have two pairs of equal and opposite angles, and that the four angles in any quadrilateral MUST add up to 360 degrees.
Because the angles given are different, we know that they are supplementary and the other two missing angles MUST be the same.

This question is very simple to answer if you remember that ALL paralellograms have two pairs of equal and opposite angles, and that the four angles in any quadrilateral MUST add up to 360 degrees.
Because the angles given are different, we know that they are supplementary and the other two missing angles MUST be the same.
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Given: Rectangle
with diagonals
and
intersecting at point
.
True or false:
must be a right angle.
Given: Rectangle with diagonals
and
intersecting at point
.
True or false: must be a right angle.
The diagonals of a parallelogram are perpendicular - and, consequently,
is a right angle. - if and only if the parallelogram is a rhombus, a figure with four sides of equal length. Not all rectangles have four congruent sides. Therefore,
need not be a right angle.
The diagonals of a parallelogram are perpendicular - and, consequently, is a right angle. - if and only if the parallelogram is a rhombus, a figure with four sides of equal length. Not all rectangles have four congruent sides. Therefore,
need not be a right angle.
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Given: Regular Pentagon
with center
. Construct segments
and
to form Quadrilateral
.
True or false: Quadrilateral
is a parallelogram.
Given: Regular Pentagon with center
. Construct segments
and
to form Quadrilateral
.
True or false: Quadrilateral is a parallelogram.
Below is regular Pentagon
with center
, a segment drawn from
to each vertex - that is, each of its radii drawn.

The measure of each angle of a regular pentagon can be calculated by setting
equal to 5 in the formula

and evaluating:

Specifically,

By symmetry, each radius bisects one of these angles. Specifically,

By the Same-Side Interior Angles Theorem, consecutive angles of a parallelogram are supplementary - that is, their measures total
. However,
,
violating these conditions. Therefore, Quadrilateral
is not a parallelogram.
Below is regular Pentagon with center
, a segment drawn from
to each vertex - that is, each of its radii drawn.
The measure of each angle of a regular pentagon can be calculated by setting equal to 5 in the formula
and evaluating:
Specifically,
By symmetry, each radius bisects one of these angles. Specifically,
By the Same-Side Interior Angles Theorem, consecutive angles of a parallelogram are supplementary - that is, their measures total . However,
,
violating these conditions. Therefore, Quadrilateral is not a parallelogram.
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Given: Parallelogram
such that
.
True or false: Parallelogram
must be a rectangle.
Given: Parallelogram such that
.
True or false: Parallelogram must be a rectangle.
A rectangle is a parallelogram with four right angles.
Consecutive angles of a parallelogram are supplementary. If one angle of a parallelogram is given to be right, then its neighboring angles, being supplementary to a right angle, are right as well; also, opposite angles of a parallelogram are congruent, so the opposite angle is also right. All four angles must be right, making the parallelogram a rectangle by definition.
A rectangle is a parallelogram with four right angles.
Consecutive angles of a parallelogram are supplementary. If one angle of a parallelogram is given to be right, then its neighboring angles, being supplementary to a right angle, are right as well; also, opposite angles of a parallelogram are congruent, so the opposite angle is also right. All four angles must be right, making the parallelogram a rectangle by definition.
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Given: Quadrilateral
such that
and
.
True or false: It follows that Quadrilateral
is a parallelogram.
Given: Quadrilateral such that
and
.
True or false: It follows that Quadrilateral is a parallelogram.
, making
and
supplementary. By the Converse of the Same Side Interior Angles Theorem, , it does follow that
. However, without knowing the measures of the other two angles, nothing further can be concluded about Quadrilateral
. Below are a parallelogram and a trapezoid, both of which have these two angles of these measures.

, making
and
supplementary. By the Converse of the Same Side Interior Angles Theorem, , it does follow that
. However, without knowing the measures of the other two angles, nothing further can be concluded about Quadrilateral
. Below are a parallelogram and a trapezoid, both of which have these two angles of these measures.
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Given: Parallelogram
such that
and
.
True or false: It follows that Parallelogram
is a rectangle.
Given: Parallelogram such that
and
.
True or false: It follows that Parallelogram is a rectangle.
By the Same-Side Interior Angles Theorem, consecutive angles of a parallelogram can be proved to be supplementary - that is, their angle measures total
. Specifically,
and
are a pair of supplementary angles. Since they are also congruent, it follows that both are right angles. For the same reason,
and
are also right angles. The parallelogram, having four right angles, is a rectangle by definition.
By the Same-Side Interior Angles Theorem, consecutive angles of a parallelogram can be proved to be supplementary - that is, their angle measures total . Specifically,
and
are a pair of supplementary angles. Since they are also congruent, it follows that both are right angles. For the same reason,
and
are also right angles. The parallelogram, having four right angles, is a rectangle by definition.
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A parallelogram contains 2 angles measuring 135 and 45. What are the measures of the other 2 angles?
A parallelogram contains 2 angles measuring 135 and 45. What are the measures of the other 2 angles?
Parallelograms have angles totalling 360 degrees, but also have matching pairs of angles at the ends of diagonals. Therefore the 2 additional angles must match the 2 given in the question.
Parallelograms have angles totalling 360 degrees, but also have matching pairs of angles at the ends of diagonals. Therefore the 2 additional angles must match the 2 given in the question.
Compare your answer with the correct one above