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 \(x+33^{\circ}+38^{\circ}=180^{\circ}\).

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

\(x = 180^{\circ}-(33^{\circ}+38^{\circ})=180^{\circ}-71^{\circ}=109^{\circ}\).

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 \(m\angle1 + 109^{\circ}=180^{\circ}\).

Step4: Solve for \(m\angle1\)

\(m\angle1=180^{\circ}-109^{\circ}=71^{\circ}\).

Answer:

\(71\)