Question

part 1 of 2 for the figure shown, find m∠1 and m∠2. (the figure is not drawn to scale.) m∠1 = <box>°

Explanation:

Step1: Use exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. For the triangle with angles \(28^{\circ}\) and \(\angle1\), the exterior angle is \(59^{\circ}\). So, \(m\angle1+28^{\circ}=59^{\circ}\).

Step2: Solve for \(m\angle1\)

Subtract \(28^{\circ}\) from both sides of the equation \(m\angle1 + 28^{\circ}=59^{\circ}\). We get \(m\angle1=59^{\circ}-28^{\circ}\).

Step3: Calculate the value of \(m\angle1\)

\(m\angle1 = 31^{\circ}\).

Step4: Find \(m\angle2\)

\(\angle2\) and the \(59^{\circ}\) angle are vertical angles. Vertical angles are equal. So \(m\angle2 = 59^{\circ}\).

Answer:

\(m\angle1 = 31^{\circ}\), \(m\angle2 = 59^{\circ}\)