Question

Triangle FGH is a right triangle. Angle G is a right angle, m∠F = 9x – 1, and m∠H = 3x + 7. What is m∠F?

Answer 1

the angles of a triangle must add up to 180 degrees.

G = 90 (because it's a right angle)
F = 9x - 1
H = 3x + 7

90 + (9x - 1) + (3x + 7) = 180
(9x - 1) + (3x + 7) = 90
12x + 6 = 90
12x = 84
x = 7

now that we have x, we can find out the measure of angle F.

9(7) - 1
63 - 1
62

angle F is 62 degrees

Answer 2

interior angles of a triangle add up to 90 degrees

< F + < G + < H = 180
9x - 1 + 90 + 3x + 7 = 180
12x + 96 = 180
12x = 180 - 96
12x = 84
x = 84/12
x = 7

so < F = 9x - 1 = 9(7) - 1 = 63 - 1 = 62 <=====
< G = 90
< H = 3x + 7 = 3(7) + 7 = 21 + 7 = 28
added : 62 + 90 + 28 = 180