How to Solve Parallel Lines and Transversals Problems? (+FREE Worksheet!)

How to solve parallel lines and transversals problems, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

Parallel Lines and Transversals, Example 2:

Solution:

The two angles (75^circ) and (11x-2) are equal. (11x-2=75)
Now, solve for (x: 11x-2+2=75+2→ 11x=77→x=frac{77}{11}→x=7)

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Parallel Lines and Transversals, Example 3:

In the following diagram, two parallel lines are cut by a transversal. What is the value of (x)?

Solution:

The two angles (7x-35) and (3x+45) are equivalents.
That is: (7x-35=3x+45)
Now, solve for (x: 7x-35+35=3x+45+35 →)
(7x=3x+80→7x-3x=3x+80-3x→4x=80→x=frac{80}{4}→x=20)

Parallel Lines and Transversals, Example 4:

In the following diagram, two parallel lines are cut by a transversal. What is the value of (x)?

Solution:

The two angles (3x-27) and (-x+33) are equivalents.
That is: (3x-27=-x+33)
Now, solve for (x: 3x-27+27=-x+33+27 →)
(3x=-x+60→3x+x=-x+60+x→4x=60→x=frac{60}{4}→x=15)

Exercises for Parallel Lines and Transversals

Simplifying Fractions

Find missing angles with Parallel Lines and Transversals.

1.Find the measure of the angle indicated.

2. Solve for (x).

3. Find the measure of the angle indicated.

4. Solve for (x).

1.(color{blue}{110^circ})

2.(color{blue}{x=8})

3. (color{blue}{84^circ})

4.(color{blue}{x=5})

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