Parallel Lines cut by a Transversal
Practice Problems
For what value of x will lines l and j be parallel?
Since the labeled angles are alternate interior ones, they are equal.
x5 = 60
x= 65
Lines P and V are parallel, what is the value of x?
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 =$$ \frac{165}{5} = 33 $$

Lines M and N are parallel, what is the value of x?
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 =$$ \frac{160}{8} = 20$$

In the picture below $$ \overline{CD} \parallel \overline{EF}$$ ,$$ \overline{AB}$$ is a transversal, $$ m\angle DGH = 2x $$ and $$ m \angle FHB = 5x51$$.
Find the measure, in degrees, of $$ \angle BHE $$.
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)
Answer: 146
