Question

two parallel lines are crossed by a transversal. if m∠6 = 123.5°, then m∠1 is 56.5°. 67.5°. 123.5°. 136.5°.

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

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

Answer:

\( 56.5^\circ \) (the first option: 56.5°)