Question

1. two parallel lines are cut by a transversal. suppose ∠1 and ∠2 are corresponding angles and that ( mangle1 = (10x + 5)^circ ) and ( mangle2 = (9x + 13)^circ ). what is ( mangle2 )?

Explanation:

Step1: Recall Corresponding Angles Postulate

Corresponding angles formed by parallel lines and a transversal are equal. So, \( m\angle1 = m\angle2 \).

Step2: Set Up the Equation

Substitute the given expressions: \( 10x + 5 = 9x + 13 \).

Step3: Solve for \( x \)

Subtract \( 9x \) from both sides: \( 10x - 9x + 5 = 9x - 9x + 13 \), which simplifies to \( x + 5 = 13 \). Then subtract 5 from both sides: \( x = 13 - 5 = 8 \).

Step4: Find \( m\angle2 \)

Substitute \( x = 8 \) into \( m\angle2 = (9x + 13)^\circ \): \( 9(8) + 13 = 72 + 13 = 85 \).

Answer:

\( 85^\circ \)