Question

3 topic assessment form a1. what type of lines are coplanar and do not intersect?a. parallelb. perpendicularc. segmentsd. transversalfor items 2-5, lines $ell$ and $m$ are intersected by transversal $t$. $ell parallel m$2. select all the angles that are supplementary to $angle 1$.$square$ a. $angle 3LXB0square$ c. $angle 5LXB1square$ e. $angle 7LXB2square$ b. $angle 2LXB3square$ d. $angle 4LXB4square$ f. $angle 8$4. complete the following plan to prove that $angle 3 cong angle 6$.use the same-side interior angles postulate to show that $angle 3$ is supplementary to $\boldsymbol{\fbox{180}}$.show $angle 6$ and $\boldsymbol{\fbox{}}$ are $\boldsymbol{\fbox{}}$ because they form a $\boldsymbol{\fbox{}}$.since $angle 3$ and $angle 6$ are $\boldsymbol{\fbox{}}$ to the same angle, they are congruent to each other.5. if $mangle 2 = 112$, what is $mangle 7$?$mangle 7 = \boldsymbol{\fbox{}}$6. select all the true statements given the figure.$square$ a. $mangle 4 = mangle 2LXB5square$ c. $mangle 4 = 180 - mangle 3LXB6square$ e. $mangle 4 = mangle 3 + mangle 1$for items 7-9, use the figure shown.7. what is $x$?a. 28b. 44c. 136d. 2248. what is $y$?$y = \boldsymbol{\fbox{}}$9. select all the true statements.$square$ a. $x = yLXB7square$ c. $y = zLXB8square$ e. $y + z = 180$

Explanation:

Step1: Solve Q1 (Line definition)

Parallel lines are coplanar, non-intersecting.

Step2: Solve Q2 (Supplementary angles)

$\angle1$ is supplementary to angles that sum to $180^\circ$ with it: $\angle4, \angle6, \angle2, \angle8$.

Step3: Solve Q3 (Congruent angles)

$\angle5$ is congruent to corresponding/alternate angles: $\angle1, \angle3, \angle7$.

Step4: Solve Q4 (Proof plan)

1. Same-Side Interior: $\angle3$ supplementary to $\angle2$.
2. $\angle6$ and $\angle2$ are supplementary (linear pair, form straight angle).
3. $\angle3$ and $\angle6$ are supplementary to same angle.

Step5: Solve Q5 (Angle relationship)

$\angle2$ and $\angle7$ are alternate interior angles, so $m\angle7=m\angle2=112$.

Step6: Solve Q6 (Triangle angle rules)

• A. $\angle4=\angle2$ (exterior angle not equal to remote interior) → False
• B. $\angle4=\angle1+\angle2$ (Exterior Angle Theorem) → True
• C. $\angle4=180-\angle3$ (linear pair) → True
• D. $\angle4=\angle1+\angle2+\angle3$ → False
• E. $\angle4=\angle3+\angle1$ → False

Step7: Solve Q7 (Triangle sum)

$x=180-(82+54)=44$

Step8: Solve Q8 (Exterior angle)

$y=82+54=136$

Step9: Solve Q9 (Angle relationships)

• A. $x=y$ → False
• B. $x+y=180$ → False
• C. $y=z$ (vertical angles) → True
• D. $x+z=180$ → False
• E. $y+z=180$ → False

Answer:

1. A. parallel
2. B. $\angle4$, D. $\angle6$, F. $\angle8$
3. A. $\angle1$, C. $\angle3$, E. $\angle7$

4.

• $\angle2$
• $\angle2$
• supplementary
• straight angle
• supplementary

1. $112$
2. B. $m\angle4 = m\angle1 + m\angle2$, C. $m\angle4 = 180 - m\angle3$
3. B. 44
4. $136$
5. C. $y = z$