Question

1. find x.

f x + 11 g
3x + 1
e h

Explanation:

Step1: Set up equation

Since the two - segments created by the angle bisector are proportional (assuming EG is the angle bisector of ∠FEH and FG and GH are perpendicular to the sides of the angle), we can set up the equation \(x + 11=3x + 1\).

Step2: Solve for x

Subtract \(x\) from both sides: \(11 = 2x+1\). Then subtract 1 from both sides: \(10 = 2x\). Divide both sides by 2: \(x = 5\).

Step3: Find FG

Substitute \(x = 5\) into the expression for FG. FG \(=x + 11\), so FG \(=5 + 11=16\).

Answer:

\(x = 5\), FG \(=16\)