ACT Math : How to find an angle in a parallelogram

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #11 : How To Find An Angle In A Parallelogram

Parallelogram_6

 is a parallelogram. Find .

Possible Answers:

Correct answer:

Explanation:

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

Parallelogram_8

 is a parallelogram. Find .

Possible Answers:

Correct answer:

Explanation:

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 ?

Screen_shot_2013-07-15_at_9.42.14_pm

Possible Answers:

Correct answer:

Explanation:

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:

2= x = 130°

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