All ACT Math Resources
Example Questions
Example Question #302 : Act Math
Given the height of a trapezoid is and a base length is
, what is the length of the other base if the area of the trapezoid is
?
Write the formula used to find the area of a trapezoid.
Substitute the given information to the formula and solve for the unknown base.
Example Question #1 : How To Find The Length Of The Side Of A Trapezoid
is an isosceles trapezoid that is bisected by
.
. If
,
, and
, then what is the length of
?
We know that all three horizontal lines are parallel to one another. By definition, we can set up a ratio between the lengths of the sides provided to us in the question and the lengths of the two parallel lines:
Once we substitute the given information, we get
We cross multiply to solve for EF
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 #1 : Parallelograms
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 #3 : How To Find An Angle In A Parallelogram
In parallelogram ,
. What is
?
In a parellelogram, consecutive angles are supplementary.
Example Question #2 : How To Find An Angle In A Parallelogram
In parallelogram ,
. What is
?
In a parallelogram, opposite angles are congruent.
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.
Example Question #1 : 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
.
All ACT Math Resources
