# Parallel and Perpendicular Lines - How to Find x

## Parallel and Perpendicular Lines - Find x - How it Works - Video

### Example 1a Example 1a:

Since we have two lines that are parallel with a transverse line, angle 1 and angel 5 are congruent, because they are corresponding angles.

Now we can set the two expressions equal, 2x + 4° = 5x - 155°.

Then we subtract the term (2x) on both sides ==> 4° = 3x - 155°.

Now we add the term 155° to both sides ==> 159° = 3x.

Finally we divide both sides by 3 ==> x = 53. So the final answer is x = 53.

### Example 1b Example 1b:

In order to find angle 8, we substitute the value x = 53 back into the expression for angle 1. We can do that because angle 1 is congruent to angle 5 because they are corresponding angles. Then we use the fact that angle 5 and angle 8 are vertical angles.

Let's find angle 8. First, we substitute x = 53 into angle 1 ==> 2(53) + 4.

We multiply the 2 and the 53 and add the 4 ==> 106 + 4 ==> 110.

So the final answer is m<8 = 110°.

### Example 2a Example 2a:

Since we have two lines that are parallel with a transverse line, angle 1 and angel 6 are supplementary, equal to 180°. The reason is that angle 1 and angle 5 are congruent because they are Corresponding Angles. And angle 5 and angle 6 are also supplementary. We can exchange angle 1 for angle 5 ==> angle 1 and angle 6 are supplementary.

Now we set angle 1 and angle 6 = 180° ==> 3x + 37° + 6x - 28° = 180°.

Next we add the like terms 3x and 6x ==> 9x + 37° - 28° = 180°.

Next we add the like terms 37 and -28 ==> 9x + 9° = 180°.

Next we subtract 9° on both sides ==> 9x = 171°.

Finally we divide both sides by 9 ==> x = 19.

### Example 2b Example 2b:

In order to find angle 3, we substitute the value x = 19 back into the expression for angle 1. Then we use the fact angle 3 and angle 1 form a linear pair, 180°.

Now we substitute x = 19 into angle 1 ==>3(19) + 37.

We multiply the 3 and 19 and add the 37 ==> 57 + 37 ==> 94°. So angle 1 is 94° which means angle 6 is 86° since they are supplementary.

Since angle 3 and angle 6 are congruent because they are Alternate Interior Angles, we can exchange the information that we about angle 6 for angle 3. Since angle 6 is 86°, we know that angle is 86°.

So our final is m<3 = 86°.

## Live Worksheet

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