Question

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

Short answer

The obtained conclusion is $\mathit{x}\mathbf{=}\mathbf{12}\mathbf{°}$.

Step-by-step solution

Step 1. Observe the provided figure

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

Step 2. Fill the second blank of reasons

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

Step 3. Use the observation

The angles that are positioned inside are having a measurement of if they are added. According to the figure $\left(x^2\right)°$and $3x°$are representing the interior angles so make an equation by using this.

$\left(x^2\right)°+3x°=180°$

Step 4. Determine the value of x

Determine the value of x by factoring the obtained equation.

$\left(x^2\right)+3x=180$

$x^2+15x-12x-180=0$

$x\left(x+15\right)-12\left(x+15\right)=0$

$\left(x-12\right)\left(x+15\right)=0$

$x=12,-15$

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 $x=12°$.