Question

using angle relationships to find variable
find the value of x that makes a || b.
74°
a
(9x + 11)°
b
a. what is the angle pair relationship?
b. select the correct equation
c. x =

Explanation:

Step1: Identify angle - pair relationship

When two parallel lines \(a\parallel b\) are cut by a transversal, the given angles \(74^{\circ}\) and \((9x + 11)^{\circ}\) are congruent (they are alternate interior angles).

Step2: Set up the equation

Since the alternate interior angles are equal, we have the equation \(9x+11 = 74\).

Step3: Solve the equation for \(x\)

Subtract \(11\) from both sides of the equation:

$$
LATEXBLOCK0
$$

Divide both sides by \(9\):

$$ x=\frac{63}{9}=7 $$

Answer:

a. Alternate interior angles.
b. \(9x + 11=74\)
c. \(x = 7\)