1. Unit 2 – Similarity, Congruence, and Proofs
Review Quiz #8
Proving Theorems about
Lines and Angles

2. Question 1
In the diagram below, ∠1 and ∠2 are a linear pair. Find m∠1 if m∠1= 2x −9 and m∠2=10x +9.
21°

3. Find m∠4 in the diagram below if m∠2= 9(x +6) and m∠4 = 2(5x +21) .
Question 2
Find m∠4 in the diagram below if m∠2= 9(x +6) and m∠4 = 2(5x +21) .
162°

4. Question 3
In the diagram below, l is the transversal of the parallel lines m and n. Find m∠3 if m∠4 =5(x +11) and m∠5=11x −17 .
65°

5. Question 4
In the diagram below, l is the transversal of the parallel lines m and n. Find m∠8 if m∠2= 3x + 46 and
m∠8= 4x .
24°

6. Question 5
In the diagram below, l is the transversal of the parallel lines m and n. Find m∠5 if m∠3= 2(3x − 4) and
m∠5= 5(3x + 4) .
140°

7. Question 6
If m∠1= 2x −9 and m∠2=10x −3, find m∠4 given that lines k and l intersect as shown below.
157°

8. Question 7
If m∠1= 4x and m∠4 =3x −1 in the diagram below, find m∠2 if ∠3 is a right angle.
38°

9. Question 8
If m∠1= x +7, m∠2= 2(x +2) , and m∠4 = 2(x +13) in the diagram below, find m∠4 .
56°

10. Question 9
In the proof of the Vertical Angles Theorem below, what are the reasons for the statements listed? Refer to the diagram given. In the diagram, ∠3 and ∠1 form a linear pair and ∠1 and ∠4 form a linear pair. Prove that ∠3 ≅ ∠4 .
Given
Supplement Theorem
Angles supplementary to the same angles or to congruent angles are congruent.

11. ∠DBA≅∠DBC ; Reflexive Property; ∆EBA≅∆EBC
Question 10
Given the diagram and the information below, determine what information is missing from the proof.
∠DBA≅∠DBC ; Reflexive Property; ∆EBA≅∆EBC

12. Question 11
There are two sets of parallel lines in the diagram below. Find m∠2 if m∠1=10x − 4 and m∠3= 7x +20 .
76°

13. Find m∠1 if m∠2= 5x and m∠3= 6x −7 .
Question 12
Find m∠1 if m∠2= 5x and m∠3= 6x −7 .
85°

14. Find m∠2 if m∠1= 5x +12 and m∠3= 4x −12 .
Question 13
Find m∠2 if m∠1= 5x +12 and m∠3= 4x −12 .
68°

15. Find m∠3 if m∠1= 3x +1 and m∠2= 2(x +7).
Question 14
Find m∠3 if m∠1= 3x +1 and m∠2= 2(x +7).
40°

16. Question 15
Given two sets of parallel lines in the diagram below, what is the relationship between ∠6 and ∠15 ?
∠6≅∠11 since they are alternate exterior angles and alternate exterior angles are congruent. Then, by corresponding angles, ∠11≅∠15 . Therefore, ∠6≅∠15 by the Transitive Property.