All ACT Math Resources
Example Questions
Example Question #11 : 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. Because we have three variables, we will need three equations.
1.
2.
3.
Start with equation 1.
Now simplify equation 2.
Finally, simplify equation 3.
Note that we can plug this simplified equation 3 directly into the simplified equation 2 to solve for .
Now that we have , we can solve for using equation 1.
With , we can solve for using equation 3.
Now that we have and , we can solve for .
Example Question #12 : 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 #321 : Plane Geometry
In the parallellogram, what is the value of ?
Opposite angles are equal, and adjacent angles must sum to 180.
Therefore, we can set up an equation to solve for z:
(z – 15) + 2z = 180
3z - 15 = 180
3z = 195
z = 65
Now solve for x:
2z = x = 130°