Question

find the measures of the numbered angles.

Explanation:

Step1: Find \(m\angle1\)

Use the triangle angle - sum theorem (\(180^{\circ}\) in a triangle).
\(m\angle1=180^{\circ}-58^{\circ}-39^{\circ}\)
\(m\angle1 = 83^{\circ}\)

Step2: Find \(m\angle2\)

\(\angle1\) and \(\angle2\) are supplementary (\(\angle1+\angle2 = 180^{\circ}\)).
\(m\angle2=180^{\circ}-m\angle1\)
\(m\angle2=180^{\circ}-83^{\circ}=97^{\circ}\)

Step3: Find \(m\angle3\)

Use the triangle angle - sum theorem again.
\(m\angle3=180^{\circ}-m\angle2 - 35^{\circ}\)
\(m\angle3=180^{\circ}-97^{\circ}-35^{\circ}=48^{\circ}\)

Answer:

\(m\angle1 = 83^{\circ},m\angle2 = 97^{\circ},m\angle3 = 48^{\circ}\) (the second option)