Question

1. find the m∠ebc

Explanation:

Step1: Identify angle - relationship

Assume lines AD and FG are parallel. Then, angles EBC and BCH are corresponding angles (if AD || FG), so \(2x=3x - 20\).

Step2: Solve the equation for x

Subtract \(2x\) from both sides of the equation \(2x=3x - 20\):
\[2x-2x=(3x - 20)-2x\]
\[0=x - 20\]
Add 20 to both sides: \(x = 20\).

Step3: Find the measure of angle EBC

Since \(m\angle EBC=2x\), substitute \(x = 20\) into the expression. Then \(m\angle EBC=2\times20=40^{\circ}\).

Answer:

\(40^{\circ}\)