Answer:
The answer to your question is ∠FSH = 42°; ∠NSF = 78°; ∠NSH = 120°
Explanation:
Data
∠ FSH = 5x - 8
∠NSF = 9x - 12
∠NSH = 10x + 20
Process
1.- Write a equation to solve this problem
∠NSH = ∠NSF + ∠FSH
2.- Substitute values
10x + 20 = 9x - 12 + 5x - 8
3.- Solve for x
10 x - 9x - 5x = - 12 - 8 - 20
10x - 14x = - 12 - 28
- 4x = - 40
x = -40 / -4
x = 10
4.- Find the measure of all three angles
∠FSH = 5(10) - 8
= 50 - 8
= 42°
∠NSF = 9x - 12
= 9(10) - 12
= 90 - 12
= 78°
∠NSH = 10(10) + 20
= 100 + 20
= 120°
5.- Check the answers
120° = 78° + 42°
120° = 120°
The answers are correct