Question

what is m∠1? m∠1 = °

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Calculate the third - interior angle of the triangle

Let the third - interior angle of the triangle be \(x\). Then \(x+57^{\circ}+35^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-(57^{\circ}+35^{\circ})=180^{\circ}-92^{\circ}=88^{\circ}\).

Step3: Use the linear - pair property

The angle \(m\angle1\) and the third - interior angle \(x\) form a linear pair. A linear pair of angles sums to 180°. So \(m\angle1=180^{\circ}-x\).
Since \(x = 88^{\circ}\), then \(m\angle1=180^{\circ}-88^{\circ}=92^{\circ}\).

Answer:

92