Question

8 in △fgh, m∠f = m∠h, gf = x + 40, hf = 3x - 20, and gh = 2x + 20. the length of gh is 1) 20 2) 40 3) 60 4) 80

Explanation:

Step1: Identify isosceles - triangle property

Since \(m\angle F=m\angle H\) in \(\triangle FGH\), then \(GF = GH\) (sides opposite equal angles in a triangle are equal).
\(x + 40=2x + 20\)

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(40=x + 20\).
Then subtract 20 from both sides: \(x=20\).

Step3: Find the length of \(GH\)

Substitute \(x = 20\) into the expression for \(GH\).
\(GH=2x + 20=2\times20+20=40 + 20=60\)

Answer:

1. 60