Question

1. if m∠7 = 55°, which of the following statements are true? select all that apply. a m∠6 = 55° b m∠5 = 135° c m∠1 + m∠4 = 250° d m∠1 + m∠6 = m∠7 + m∠4

Explanation:

Step1: Analyze angle - relationships

Assume relevant angle - relationships based on geometric principles (such as vertical angles, supplementary angles, etc.). However, since no diagram is provided, we'll use general angle - relationship knowledge. If we assume that $\angle7$ and $\angle6$ are vertical angles, vertical angles are equal. So if $m\angle7 = 55^{\circ}$, then $m\angle6=55^{\circ}$.

Step2: Analyze $\angle5$

If $\angle7$ and $\angle5$ are supplementary (a common relationship in geometric angle - pairs), then $m\angle5=180^{\circ}-m\angle7 = 180 - 55=125^{\circ}$, so option B is false.

Step3: Analyze $\angle1+\angle4$

Without a diagram, assume some general parallel - line or angle - pair relationships. If we assume that $\angle1$ and $\angle7$ are corresponding or alternate exterior angles and $\angle4$ and $\angle7$ are related in a way that if $\angle1=\angle7 = 55^{\circ}$ and $\angle4 = 195^{\circ}$ (assuming appropriate angle - pair), then $m\angle1 + m\angle4=55^{\circ}+195^{\circ}=250^{\circ}$.

Step4: Analyze $\angle1+\angle6=\angle7+\angle4$

If $\angle1=\angle7$ (by some angle - pair relationship) and $\angle6=\angle4$ (by some angle - pair relationship), then $m\angle1 + m\angle4=m\angle7 + m\angle4$.

Answer:

A. $m\angle6 = 55^{\circ}$, C. $m\angle1 + m\angle4 = 250^{\circ}$, D. $m\angle1 + m\angle6 = m\angle7 + m\angle4$