Parallel Lines cut by a Transversal

Practice Problems

Since the labeled angles are alternate interior ones, they are equal.

x-5 = 60
x= 65

The red angles below are alternate exterior ones, they are equal.

This allows us to use the supplementary angles that measure (2x) and (3x+15) to set up the equation below.

2x+ 3x+15 = 180
5x + 15 = 180
5x = 165

x = $$\frac{165}{5} = 33$$

The pink angles below are same side interior ones, which means they are supplementary angles so we can set up the equation below.

3x -10+ 5x+ 30 = 180
8x + 20 = 180
8x = 160

x = $$\frac{160}{8} = 20$$

The darkened angles are corresponding and are congruent so we can set up the equation:

2x = 5x - 51
-3x = -51
x = $$\frac{-51}{-3}$$
x = 17

Now, that we know the value of x, we can determine the measure of the entire darkened angle:

• angle's measurement = 5x -51 = 5(17) -51 = 34
• $$m \angle H$$ = 180 - 54 = 146 (because they are supplementary)