Question

in the figure below, ( mangle 2 = 56^{circ} ) and ( mangle gvh = 142^{circ} ). find ( mangle 1 ).

Explanation:

Step1: Use the angle - sum property

We know that \(m\angle GJH=m\angle1 + m\angle2\).

Step2: Substitute the given values

Given \(m\angle2 = 56^{\circ}\) and \(m\angle GJH=142^{\circ}\). Then \(142^{\circ}=m\angle1 + 56^{\circ}\).

Step3: Solve for \(m\angle1\)

Subtract \(56^{\circ}\) from both sides of the equation: \(m\angle1=142^{\circ}- 56^{\circ}\).

$$m\angle1 = 86^{\circ}$$

Answer:

\(86^{\circ}\)