Question

Given: m<FSH = (5x-8)°, m<NSF=(9x-12)° and m<NSH=(10x+20)°.

Answer 1

Answer:

The answer to your question is ∠FSH = 42°; ∠NSF = 78°; ∠NSH = 120°

Step-by-step 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