Question

JG bisects FJH, FJG= (2x + 4)° and GJH = (3x -9)°
What is FJH

Answer 1

Hello from MrBillDoesMath!

Answer:

60

Discussion:

As JG bisects FJG,

FJG = GJH =>

2x + 4 = 3x-9 => subtract 2x from each side

4 = 3x -2x - 9 => simplify

4 = x - 9 => add 9 to both sides

4 + 9 = x

x = 13

Now, FJH =

FJG + GJH

(2x + 4) + (3x-9) =

5x -5 => substitute x 13

5(13) -5 =

65 - 5 =

60

Thank you,

MrB

Answer 2

Angle FJH is 60°

Explanation:

Given,

∠FJG = (2x+4)°

∠GJH = (3x-9)°,

Since, line segment JG bisects angle FJH,

So, by the property of angle bisector,

∠FJG = ∠GJH

⇒ 2x + 4 = 3x - 9

⇒ 2x = 3x - 9 - 4

⇒ 2x - 3x = -13

⇒ -x = -13

⇒ x = 13

Hence, ∠FJH = ∠FJG + ∠GJH

= 2∠FJG

= 2( 2×13 + 4)

= 2(26+4)

= 2(30)

= 60°