Question

question 14. which statements must be true about these angles? choose all that are correct. a. ∠1≅∠4 b. m∠2 + m∠4 + m∠6 = 180 c. ∠3≅∠5

Explanation:

Step1: Recall vertical - angle property

Vertical angles are congruent. $\angle1$ and $\angle4$ are vertical angles, so $\angle1\cong\angle4$.

Step2: Consider angle - sum around a point

The sum of angles around a point is $360^{\circ}$. $\angle2+\angle4+\angle6$ is half of the angles around the point, so $m\angle2 + m\angle4+m\angle6=180^{\circ}$.

Step3: Recall vertical - angle property again

$\angle3$ and $\angle5$ are vertical angles, so $\angle3\cong\angle5$.

Answer:

A. $\angle1\cong\angle4$
B. $m\angle2 + m\angle4 + m\angle6=180$
C. $\angle3\cong\angle5$