Question

1. find ( mangle fgb ) if ( mangle fgh = 162^{circ} ) and ( mangle bgh = 55^{circ} ).

Explanation:

Step1: Analyze the relationship between angles

From the figure, we know that \(m\angle FGB + m\angle BGH=m\angle FGH\) (angle - addition postulate).

Step2: Solve for \(m\angle FGB\)

We can rewrite the formula as \(m\angle FGB=m\angle FGH - m\angle BGH\).
Substitute \(m\angle FGH = 162^{\circ}\) and \(m\angle BGH = 55^{\circ}\) into the formula:
\(m\angle FGB=162^{\circ}- 55^{\circ}\)
\(m\angle FGB = 107^{\circ}\)

Answer:

\(107^{\circ}\)