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, \(x+66^{\circ}+39^{\circ}=180^{\circ}\).

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

\(x = 180^{\circ}-(66^{\circ}+39^{\circ})=180^{\circ}-105^{\circ}=75^{\circ}\).

Step3: Use the linear - pair property

Angle 1 and the third - interior angle \(x\) form a linear pair. A linear pair of angles is supplementary, meaning their sum is 180°. So, \(m\angle1 + x=180^{\circ}\).

Step4: Solve for \(m\angle1\)

\(m\angle1=180^{\circ}-x\). Substituting \(x = 75^{\circ}\), we get \(m\angle1 = 105^{\circ}\).

Answer:

\(105\)