Question

what is m∠1? m∠1 =

Explanation:

Step1: Recall triangle - angle sum property

The sum of interior angles of a triangle is 180°. Let the third - interior angle of the triangle be \(x\). So, \(x + 39^{\circ}+102^{\circ}=180^{\circ}\).

Step2: Solve for the third - interior angle \(x\)

\(x=180^{\circ}-(39^{\circ} + 102^{\circ})=180^{\circ}-141^{\circ}=39^{\circ}\).

Step3: Use the linear - pair property

\(\angle1\) and the third - interior angle \(x\) form a linear pair. A linear pair of angles sums to 180°. So, \(m\angle1 + x=180^{\circ}\).

Step4: Solve for \(m\angle1\)

Since \(x = 39^{\circ}\), then \(m\angle1=180^{\circ}-39^{\circ}=141^{\circ}\).

Answer:

141