Answer:
7. m<RST = 138°
8. m<MNP = 56°
9. m<WXZ = 130°
10. m<ABC = 118°
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°