Level 2 · Intermediate ← Back to lesson

Parallel Lines and Transversals: Practice

12 multiple-choice questions, progressively harder.

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

In the numbered diagram, $\ell\parallel m$ , $m\angle2=(5x+7)^\circ$ , and $m\angle6=(8x-20)^\circ$ . Find $x$ .

Answer choices for question 1 A $13$ B $9$ C $27$ D $3$
2

In the numbered diagram, $\ell\parallel m$ , $m\angle4=(3x+14)^\circ$ , and $m\angle5=(5x+22)^\circ$ . Find $x$ .

Answer choices for question 2 A $-4$ B $27$ C $22$ D $18$
3

In the numbered diagram, $\ell\parallel m$ , $m\angle1=(7x-8)^\circ$ , and $m\angle7=(4x+28)^\circ$ . Find $x$ .

Answer choices for question 3 A $12$ B $4$ C $20$ D $36$
4

In the numbered diagram, $\ell\parallel m$ , $m\angle2=(4x+11)^\circ$ , and $m\angle7=(6x+9)^\circ$ . Find $x$ .

Answer choices for question 4 A $1$ B $18$ C $16$ D $20$
5

In the numbered diagram, $\ell\parallel m$ and $m\angle7=121^\circ$ . Find $m\angle4$ .

Answer choices for question 5 A $121^\circ$ B $31^\circ$ C $149^\circ$ D $59^\circ$
6

For the numbered crossings, let $L=m\angle4+m\angle5$ and $R=m\angle3+m\angle6$ . Before imposing parallelism, angle addition gives $L+R=360^\circ$ . If $L=191^\circ$ , what is $R$ ?

Answer choices for question 6 A $191^\circ$ B $169^\circ$ C $180^\circ$ D $11^\circ$
7

For the numbered diagram with $\ell\parallel m$ , the proof has $m\angle1+m\angle4=180^\circ$ and $m\angle4+m\angle5=180^\circ$ . Which step establishes $\angle1\cong\angle5$ ?

Answer choices for question 7 A Assume the converse of corresponding congruence B Treat angles 1 and 5 as vertical C Subtract the common measure of angle 4 D Add all four measures at the upper vertex
8

The three-line diagram gives $\ell\parallel m$ and $m\parallel n$ . If $m\angle A=57^\circ$ , find $m\angle C$ .

Answer choices for question 8 A $123^\circ$ B $57^\circ$ C $33^\circ$ D $114^\circ$
9

Two distinct transversals $t$ and $u$ each cross parallel lines $\ell$ and $m$ . A selected angle made by $t$ at $\ell$ measures $46^\circ$ ; a selected angle made by $u$ at $\ell$ measures $81^\circ$ . At $m$ , select the angle corresponding to each of those two angles. What is the difference between the selected measures at $m$ ?

Answer choices for question 9 A $35^\circ$ B $0^\circ$ C $53^\circ$ D $127^\circ$
10

A transversal crosses two distinct coplanar lines, with no parallel condition given. Angles $A$ and $B$ are alternate interior angles. Which conclusion follows from that description alone?

Answer choices for question 10 A They must be congruent B Their measures must total 180 degrees C They are interior and on opposite sides of the transversal D They share one vertex
11

In the numbered diagram with $\ell\parallel m$ , which two proved relationships establish $\angle2\cong\angle8$ ?

Answer choices for question 11 A Angles 2 and 8 are a linear pair; angles 6 and 8 correspond B Angles 2 and 6 correspond; angles 6 and 8 are vertical C Angles 2 and 6 are vertical; angles 6 and 8 correspond D Angles 2 and 7 correspond; angles 7 and 8 are vertical
12

What is the correct order of dependence when deriving corresponding-angle congruence in this lesson?

Answer choices for question 12 A Corresponding-angle postulate, alternate angles, vertical angles B Triangle-angle sum, same-side interior sums, corresponding angles C Converse test, parallelism, corresponding-angle postulate D Angle postulate, same-side interior sums, congruent supplements

← Back to lesson