Practice Problems
Problem 1
For what value of x will lines l and j be parallel?
Since the labeled angles are alternate interior ones, they are congruent.
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)
Answer: 146
