Question

which statements must be true about these angles? choose all that are correct.
□ ∠1≅∠4
□ m∠2 + m∠4 + m∠6 = 180°
□ ∠3≅∠5
□ m∠2 + m∠3 + m∠4 = 180°
□ m∠2 + m∠3 + m∠5 = 180°

Explanation:

Step1: Recall angle - sum properties

When two lines intersect, vertical angles are equal. $\angle1$ and $\angle4$ are vertical angles, so $\angle1\cong\angle4$. Also, $\angle3$ and $\angle5$ are vertical angles, so $\angle3\cong\angle5$.

Step2: Consider linear - pair angles

$\angle2$, $\angle3$, and $\angle4$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So $m\angle2 + m\angle3+m\angle4 = 180^{\circ}$.

Step3: Analyze other angle - sum combinations

$\angle2$, $\angle3$, $\angle4$, and $\angle5$ do not form a linear - pair or a well - known angle relationship that sums to $180^{\circ}$. And $\angle2+\angle3+\angle5$ do not have a sum of $180^{\circ}$. Also, $\angle2+\angle4+\angle6$ do not form a linear - pair or a known angle relationship that sums to $180^{\circ}$.

Answer:

$\angle1\cong\angle4$, $m\angle2 + m\angle3+m\angle4 = 180^{\circ}$, $\angle3\cong\angle5$