Can someone please help me with these questions?

7. m<RST = 138°

8. m<MNP = 56°

9. m<WXZ = 130°

10. m<ABC = 118°

Step-by-step explanation:

7. m<RST = 138° (alternate exterior angles are congruent)

8. m<MNP = (a + 28)°

(a + 28)° = 2a° (alternate interior angles are congruent)

a + 28 = 2a

Collect like terms

28 = 2a - a

28 = a

m<MNP = (a + 28)°

Substitute a = 28

m<MNP = (28 + 28)° = 56°

9. m<WXZ = 5y°

5y = (2y + 78)° (alternate interior angles are congruent)

5y = 2y + 78

Collect like terms

5y - 2y = 78

3y = 78

Divide both sides by 3

y = 26

m<WXZ = 5y°

Plug in the value of y

m<WXZ = 5(26)

m<WXZ = 130°

10. m<ABC = (3n - 47)°

(3n - 47)° + (n + 7)° = 180° (same side interior angles are supplementary)

3n - 47 + n + 7 = 180

Collect like terms

4n - 40 = 180

Add 40 to both sides

4n = 180 + 40

4n = 220

Divide both sides by 4

4n/4 = 220/4

n = 55

m<ABC = (3n - 47)°

Plug in the value of n

m<ABC = 3(55) - 47 = 165 - 47

m<ABC = 118°

We know the triangle in a right triangle because of the pythagoras theorem: 5^2+12^2=13^2

25 + 144 equals 169, making it a right triangle since the equation works.

Step-by-step explanation:

I tried to explain this the best i could, hope it works :)