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Chapter 3: Q31 (page 88)

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+15x−12x−180=0

xx+15−12x+15=0

x−12x+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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