Question

in the figure, line e || line f. which statement is true? o ∠2≅∠7 o line f⊥ line g o m∠3 = 70° o m∠6 = 70°

Explanation:

Step1: Identify vertical - angle relationship

The angle of $110^{\circ}$ and $\angle5$ are vertical angles, so $\angle5 = 110^{\circ}$.

Step2: Use supplementary - angle property

Since $\angle5$ and $\angle6$ are supplementary (linear - pair), $\angle5+\angle6 = 180^{\circ}$. Substituting $\angle5 = 110^{\circ}$, we get $110^{\circ}+\angle6=180^{\circ}$, then $\angle6 = 70^{\circ}$.

Step3: Use corresponding - angle property

Because line $e\parallel$ line $f$, $\angle3$ and $\angle6$ are corresponding angles. So $\angle3=\angle6 = 70^{\circ}$.

Step4: Analyze other options

• $\angle2$ and $\angle7$ are not congruent as they are not corresponding, alternate - interior or alternate - exterior angles.
• Since the angle between line $f$ and line $g$ is $110^{\circ}$, line $f$ is not perpendicular to line $g$.
• We have shown that $m\angle6 = 70^{\circ}$, but the correct statement based on angle - relationships and parallel lines among the options is $m\angle3 = 70^{\circ}$.

Answer:

C. $m\angle3 = 70^{\circ}$