Question

5 fill in the blank 1 point (overline{gi}) bisects (angle fgh) such that (mangle fgi = 2x + 20) and (mangle igh = 5x - 37). draw a diagram of the description, then find the value of (x). (x = ) type your answer...

Explanation:

Step1: Recall angle bisector definition

An angle bisector divides an angle into two equal angles. So, \( m\angle FGI = m\angle IGH \).

Step2: Set up the equation

Since \( m\angle FGI = 2x + 20 \) and \( m\angle IGH = 5x - 37 \), we set them equal: \( 2x + 20 = 5x - 37 \).

Step3: Solve for x

Subtract \( 2x \) from both sides: \( 20 = 3x - 37 \).
Add 37 to both sides: \( 57 = 3x \).
Divide by 3: \( x = \frac{57}{3} = 19 \).

Answer:

19