Question

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

Explanation:

Step1: Identify angle - pair relationships

Since line $e\parallel$ line $f$ and line $g$ is a transversal, $\angle5$ and the $110^{\circ}$ angle are vertical angles, so $m\angle5 = 110^{\circ}$.

Step2: Use the property of same - side interior angles

$\angle5$ and $\angle3$ are same - side interior angles. For parallel lines $e$ and $f$ cut by transversal $g$, same - side interior angles are supplementary. That is $m\angle3+m\angle5 = 180^{\circ}$.

Step3: Calculate the measure of $\angle3$

Substitute $m\angle5 = 110^{\circ}$ into $m\angle3+m\angle5 = 180^{\circ}$. We get $m\angle3=180 - 110=70^{\circ}$.

• Option A: $\angle5 = 110^{\circ}$, line $f$ and line $g$ do not form a right - angle, so line $f$ is not perpendicular to line $g$.
• Option C: $\angle6$ and $\angle5$ are vertical angles, so $m\angle6 = 110^{\circ}

eq70^{\circ}$.

• Option D: $\angle2$ and $\angle7$ are neither corresponding, alternate interior, nor alternate exterior angles, and there is no equality relationship between them.

Answer:

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