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°. Let the third - interior angle of the triangle be \(x\). So, \(x + 38^{\circ}+51^{\circ}=180^{\circ}\).

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

\(x=180^{\circ}-(38^{\circ} + 51^{\circ})=180^{\circ}-89^{\circ}=91^{\circ}\).

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 \(x = 91^{\circ}\), then \(m\angle1=180^{\circ}-91^{\circ}=89^{\circ}\).

Answer:

89