See explanation.
Step-by-step explanation:
1) Let’s use process of elimination to find our answer.
a) These two angles are vertical to each other, meaning they are congruent. So, ∠1 and ∠3 are not supplementary angles.
b) ∠2 and ∠6 are congruent, since they both are on the same place as each other, which makes them corresponding angles. So, ∠2 and ∠6 are not supplementary angles.
c) ∠4 and ∠6 are alternate interior angles, meaning they are congruent. So, they are not supplementary angles.
d) ∠7 and ∠8 share the same straight line and the same median, meaning they are supplementary.
D is the correct answer.
2) Again, process of elimination.
a) ∠1 and ∠3 are vertical angles, not alternate exterior.
b) ∠2 and ∠6 are congruent angles since they are corresponding, but not alternate exterior.
c) ∠4 and ∠6 are alternate interior angles, not alternate exterior angles.
d) ∠7 and ∠1 are alternate exterior angles.
D is the correct answer.
3) Process of elimination.
a) ∠1 and ∠4 are supplementary angles, meaning they aren’t congruent.
b) ∠4 and ∠5 are again, supplementary. So, they aren’t congruent.
c) ∠1 and ∠5 are congruent angles since they are corresponding angles.
d) ∠7 and ∠8 both share the same straight line and median, so they are supplementary, not congruent.
C is the correct answer.
4)
a) ∠4 and ∠8 are corresponding angles since they are both in the exact same place as each other.
b) ∠4 and ∠6 are alternate interior angles, not corresponding angles.
c) ∠1 and ∠2 both share the same straight line and the same median, meaning they are supplementary. So, they are not corresponding angles.
d) ∠2 and ∠8 are alternate exterior angles, and not corresponding.
A is the correct answer.
5) ∠1 and ∠2 are supplementary angles since they share the same straight line and median. So, their sum is 180°.
If m∠2=70°,
m∠1=110°
C is the correct answer.
6) ∠2 and ∠4 are vertical angles, meaning they are congruent.
If m∠2=70°,
m∠4=70°.
A is the correct answer.
7) ∠2 and ∠6 are corresponding angles, meaning they are congruent.
If m∠2=70°
m∠6=70°.
D is the correct answer.
8) ∠2 and ∠3 both share the same straight line and median, meaning they are supplementary and have a sum of 180°.
If m∠2=70°,
m∠3=110°
B is the correct answer.
9) ∠6 and ∠7 are supplementary angles, meaning they share the same straight line and median. So, their sum is 180°.
If m∠6=106°,
m∠7=74°
B is the correct answer.
10) ∠6 and ∠1 are both exterior angles, but they are both on the same straight lines. So, their sum is 180°.
If m∠6=106°,
m∠1=74°
B is the correct answer.
