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 \(x+51^{\circ}+82^{\circ}=180^{\circ}\).

Step2: Calculate the third - interior angle

\(x = 180^{\circ}-(51^{\circ}+82^{\circ})=180^{\circ}-133^{\circ}=47^{\circ}\).

Step3: Use the linear - pair property

\(\angle1\) and the third - interior angle of the triangle form a linear pair. A linear pair of angles sums to 180°. So \(m\angle1 = 180^{\circ}-47^{\circ}\).

Step4: Find the measure of \(\angle1\)

\(m\angle1=133^{\circ}\).

Answer:

\(133\)