Question

select all the true statements.a. $angle3 cong angle2$ because they are alternate interior angles.b. $mangle1 + mangle3 = 180$ 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 $mangle1 + mangle3 = 180$.e. $angle1 cong angle3$ because they are vertical angles.

Explanation:

Step1: Analyze Option A

$\angle3$ and $\angle2$ are vertical angles, not alternate interior angles. So A is false.

Step2: Analyze Option B

$\angle1$ and $\angle3$ form a straight angle (180°).
$m\angle1 + m\angle3 = 180^\circ$
So B is true.

Step3: Analyze Option C

$\angle3$ and $\angle6$ are alternate interior angles, so they are congruent.
$\angle3 \cong \angle6$
So C is true.

Step4: Analyze Option D

From Step2, $m\angle1 + m\angle3 = 180^\circ$; from Step3, $\angle3 \cong \angle6$ so $m\angle3 = m\angle6$. Substitute: $m\angle1 + m\angle6 = 180^\circ$, meaning they are supplementary. So D is true.

Step5: Analyze Option E

$\angle1$ and $\angle3$ are adjacent angles forming a straight line, not vertical angles. Vertical angles are opposite each other, so E is false.

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 $m\angle1 + m\angle3 = 180$.