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Find the value of x that makes the lines shown in red parallel.

Short Answer

Expert verified

The obtained conclusion is x=12°.

Step by step solution

01

Step 1. Observe the provided figure

The provided figure represents that the lines m and n are having a parallel connection between them.

02

Step 2. Fill the second blank of reasons

As the angles 1and 3are the vertical angles which are having the same measurement so they are congruent.

03

Step 3. Use the observation

The angles that are positioned inside are having a measurement of if they are added. According to the figure x2°and 3x°are representing the interior angles so make an equation by using this.

x2°+3x°=180°

04

Step 4. Determine the value of x

Determine the value of x by factoring the obtained equation.

x2+3x=180

x2+15x12x180=0

xx+1512x+15=0

x12x+15=0

x=12,15

05

Step 5. Make the conclusion

The negative value of x cannot be considered because it will result in a negative angle and an angle is always positive so the value of x=12°.

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