Question

in this figure, ( overline{ab} parallel overline{cd} ) and ( mangle4 = 85^{circ} ).
what is ( mangle5 )?
enter your answer in the box.

Explanation:

Step1: Identify angle relationship

Since \( \overline{AB} \parallel \overline{CD} \) and the transversal creates consecutive interior angles, \( \angle 4 \) and \( \angle 5 \) are consecutive interior angles. Consecutive interior angles are supplementary, meaning their measures add up to \( 180^\circ \).

Step2: Calculate \( m\angle 5 \)

We know \( m\angle 4 = 85^\circ \) and \( m\angle 4 + m\angle 5 = 180^\circ \). So we solve for \( m\angle 5 \):

$$ m\angle 5 = 180^\circ - m\angle 4 $$

Substitute \( m\angle 4 = 85^\circ \):

$$ m\angle 5 = 180^\circ - 85^\circ = 95^\circ $$

Answer:

\( 95^\circ \)