Question

two parallel lines are crossed by a transversal. if ( mangle6 = 123.5^{circ} ), then ( mangle1 ) is ( 56.5^{circ} ). ( 67.5^{circ} ). ( 123.5^{circ} ). ( 136.5^{circ} ).

Explanation:

Step1: Identify angle relationships

∠5 and ∠6 are supplementary (linear pair), so \( m\angle5 = 180^\circ - m\angle6 \).
\( m\angle5 = 180^\circ - 123.5^\circ = 56.5^\circ \).

Step2: Use corresponding angles (parallel lines)

∠1 and ∠5 are corresponding angles (since lines \( x \) and \( y \) are parallel, transversal creates corresponding angles). So \( m\angle1 = m\angle5 \).

Answer:

56.5° (Option: 56.5°)