Question

1. find ( mangle fgb ) if ( mangle fgh = 168^circ ) and ( mangle bgh = 59^circ ).

Explanation:

Step1: <Use angle - subtraction relationship>

We know that \(m\angle FGB=m\angle FGH - m\angle BGH\) (by the angle - subtraction postulate: if we have two angles \(\angle FGH\) and \(\angle BGH\) such that \(\angle FGH\) is composed of \(\angle FGB\) and \(\angle BGH\), then \(m\angle FGB=m\angle FGH - m\angle BGH\)).

Step2: <Substitute the given values>

Given \(m\angle FGH = 168^{\circ}\) and \(m\angle BGH=59^{\circ}\), we substitute these values into the formula: \(m\angle FGB = 168^{\circ}-59^{\circ}\).

Step3: <Calculate the result>

\(168 - 59=109\), so \(m\angle FGB = 109^{\circ}\).

Answer:

\(109^{\circ}\)