Question

classwork: complete both sides!
ex1:
a. name the angle pair:________________
b. find the value(s) of x so that m || l.
m<3 = x² - 2x
m<8 = 3x + 108

Explanation:

Step1: Identify the angle pair

The angle pair is alternate interior angles. When \(m\parallel l\), \(\angle3\) and \(\angle8\) are congruent (by the Alternate - Interior Angles Theorem).

Step2: Set up the equation

Since \(\angle3\cong\angle8\) when \(m\parallel l\), we set \(x^{2}-2x = 3x + 108\).
Rearrange the equation to get a quadratic equation: \(x^{2}-2x-3x - 108=0\), which simplifies to \(x^{2}-5x - 108 = 0\).
Factor the quadratic equation: \((x - 12)(x+9)=0\).

Step3: Solve for \(x\)

Set each factor equal to zero:

• For \(x - 12=0\), we get \(x = 12\).
• For \(x + 9=0\), we get \(x=-9\).

Answer:

a. Alternate interior angles
b. \(x = 12\) or \(x=-9\)