Question

geometry hon - garcia (lms) 2 - tteacher_s_parallel lines_p8 (lms graded) a. ∠3≅∠2 because they are alternate interior angles. b. m∠1 + m∠3 = 180 because they form a straight angle c. ∠3≅∠6 because they are alternate interior angles. d. ∠1 and ∠6 are supplementary because ∠3≅∠6 and m∠1 + m∠3 = 180 e. ∠1≅∠3 because they are vertical angles

Explanation:

Step1: Analyze option A

$\angle3$ and $\angle2$ are adjacent angles, not alternate - interior angles. So option A is incorrect.

Step2: Analyze option B

$\angle1$ and $\angle3$ form a straight - line pair. The sum of angles on a straight line is $180^{\circ}$. So $m\angle1 + m\angle3=180$ is correct.

Step3: Analyze option C

$\angle3$ and $\angle6$ are alternate - interior angles formed by two parallel lines and a transversal. So $\angle3\cong\angle6$ is correct.

Step4: Analyze option D

Since $\angle3\cong\angle6$ (alternate - interior angles) and $m\angle1 + m\angle3 = 180$ (straight - line pair), then by substitution, $\angle1$ and $\angle6$ are supplementary. So option D is correct.

Step5: Analyze option E

$\angle1$ and $\angle3$ are vertical angles. Vertical angles are congruent. So $\angle1\cong\angle3$ is correct.

Answer:

B. $m\angle1 + m\angle3 = 180$ because they form a straight angle
C. $\angle3\cong\angle6$ because they are alternate interior angles
D. $\angle1$ and $\angle6$ are supplementary because $\angle3\cong\angle6$ and $m\angle1 + m\angle3 = 180$
E. $\angle1\cong\angle3$ because they are vertical angles