Question

1. ( mangle cba = 127^{circ} ) and ( mangle cbh = 55^{circ} ). find ( mangle hba ).

Explanation:

Step1: Analyze the relationship between angles

We know that \(m\angle CBA=m\angle CBH + m\angle HBA\) (angle - addition postulate).

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

Rearrange the formula: \(m\angle HBA=m\angle CBA - m\angle CBH\).
Substitute the given values: \(m\angle HBA = 127^{\circ}-55^{\circ}\).

$$m\angle HBA=72^{\circ}$$

Answer:

\(72^{\circ}\)