Question

in the figure below, ( mangle fgh = 141^{circ} ) and ( mangle 1 = 57^{circ} ). find ( mangle 2 ).

Explanation:

Step1: Analyze the relationship between angles

We know that \(m\angle FGH=m\angle1 + m\angle2\) (angle - addition postulate).

Step2: Solve for \(m\angle2\)

Rearrange the formula to \(m\angle2=m\angle FGH - m\angle1\).
Substitute \(m\angle FGH = 141^{\circ}\) and \(m\angle1 = 57^{\circ}\) into the formula: \(m\angle2=141^{\circ}- 57^{\circ}\).

$$m\angle2 = 84^{\circ}$$

Answer:

\(84^{\circ}\)