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Example Question #1 : How To Find An Angle In A Parallelogram
In parallelogram ,
and the height is
. What is
?
We can start this problem by drawing the height and labeling the lengths with the given values.
When we do this, we can see that we have drawn a triangle inside the paralellogram including . Because we know the lengths of two sides of this triangle, we can use trigonometry to find
.
With respect to , we know the values of the opposite and hypotenuse sides of the triangle. Thus, we can use the sine function to solve for
.
Example Question #1 : How To Find An Angle In A Parallelogram
In parallelogram ,
and
. Find
.
In a parallelogram, consecutive angles are supplementary. Thus,
Example Question #3 : How To Find An Angle In A Parallelogram
is a parallelogram. Find
.
In a parallelogram, consecutive angles are supplementary (i.e. add to ) and opposite angles are congruent (i.e. equal). Using these properties, we can write a system of equations.
1.
2.
Starting with equation 1.,
Now substituting into equation 2.,
Finally, because opposite angles are congruent, we know that .
Example Question #1 : How To Find An Angle In A Parallelogram
is a parallelogram. Find
.
In a parallelogram, consecutive angles are supplementary and opposite angles are congruent. Using these properties, we can write a system of equations.
1.
2.
3.
Starting with equation 1.,
Substituting into equation 2.,
Using equation 3.,
Example Question #5 : How To Find An Angle In A Parallelogram
In parallelogram ,
. What is
?
In a parellelogram, consecutive angles are supplementary.
Example Question #6 : How To Find An Angle In A Parallelogram
In parallelogram ,
. What is
?
In a parallelogram, opposite angles are congruent.
Example Question #7 : How To Find An Angle In A Parallelogram
is a parallelogram. Find
.
In a parallelogram, consecutive angles are supplementary and opposite angles are congruent.
Example Question #8 : How To Find An Angle In A Parallelogram
In parallelogram ,
. What is
In the above parallelogram, and
are consecutive angles (i.e. next to each other). In a parallelogram, consecutive angles are supplementary, meaning they add to
.
Example Question #1 : How To Find An Angle In A Parallelogram
In parallelogram ,
. What is
?
In parallelogram ,
and
are opposite angles. In a parallelogram, opposite angles are congruent. This means these two angles are equal.
Example Question #10 : How To Find An Angle In A Parallelogram
In parallelogram , what is the sum of
and
?
In a parallelogram, consecutive angles are supplementary. and
are consecutive, so their sum is
.
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