Question

given the following parallel lines and transversal, m∠2 = 7x - 20 and m∠6 = 4x + 13. solve for x. image of two parallel horizontal lines cut by a transversal, with angles labeled 1,2,3,4 (top line) and 5,6,7,8 (bottom line) options: x = 17; x = 11; x = 3; x = 15

Explanation:

Step1: Identify angle relationship

∠2 and ∠6 are corresponding angles (parallel lines, transversal), so \( m\angle2 = m\angle6 \).

Step2: Set up equation

\( 7x - 20 = 4x + 13 \)

Step3: Solve for x

Subtract \( 4x \) from both sides: \( 3x - 20 = 13 \)
Add 20 to both sides: \( 3x = 33 \)
Divide by 3: \( x = 11 \)

Answer:

x = 11