Question

in the figure, m∠4 = 118° find the angle measure. justify each step
a. m∠8
∠4 ≅ ∠8 by select choice m∠4 = m∠8 by the definition of congruent angles, so m∠8 = 118° by select choice

Explanation:

Step1: Identify Angle Relationship

∠4 and ∠8 are corresponding angles (since the two horizontal lines are parallel, cut by a transversal). Corresponding angles are congruent.
So, ∠4 ≅ ∠8 by Corresponding Angles Postulate.

Step2: Apply Congruent Angles Definition

By the definition of congruent angles, \( m\angle4 = m\angle8 \). Given \( m\angle4 = 118^\circ \), we substitute this value.
So, \( m\angle8 = 118^\circ \) by Substitution Property.

Answer:

\( m\angle8 = 118^\circ \) (∠4 ≅ ∠8 by Corresponding Angles Postulate; \( m\angle8 = 118^\circ \) by Substitution Property as \( m\angle4 = m\angle8 \) from congruent angles definition)