Question

what is the value of x such that ℓ ∥ m? what theorem did you use to find the value?
(11x + 5)°
(9x + 35)°
a) x = 10; converse of the corresponding angles theorem
b) x = 10; consecutive interior angles converse
c) x = 15; alternate exterior angles converse
d) x = 15; alternate interior angles converse

Explanation:

Step1: Identify Angle Relationship

The angles \((11x + 5)^\circ\) and \((9x + 35)^\circ\) are alternate interior angles. For lines \(l\) and \(m\) to be parallel, alternate interior angles must be equal (Alternate Interior Angles Converse). So, set the angles equal:
\(11x + 5 = 9x + 35\)

Step2: Solve for \(x\)

Subtract \(9x\) from both sides:
\(11x - 9x + 5 = 35\)
\(2x + 5 = 35\)

Subtract 5 from both sides:
\(2x = 35 - 5\)
\(2x = 30\)

Divide by 2:
\(x = \frac{30}{2} = 15\)

Answer:

D) \(x = 15\); Alternate Interior Angles Converse