Question

1. find m∠1. 75° 75° 30° 55° 35° 40°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.
Let the three angles of the triangle be \(A = 75^{\circ}\), \(B = 75^{\circ}\), and \(C=\angle1\). Then \(A + B + C=180^{\circ}\).

Step2: Substitute the known angles

Substitute \(A = 75^{\circ}\) and \(B = 75^{\circ}\) into the equation \(A + B + C = 180^{\circ}\). We get \(75^{\circ}+75^{\circ}+\angle1=180^{\circ}\).

Step3: Solve for \(\angle1\)

First, add 75° and 75°: \(75^{\circ}+75^{\circ}=150^{\circ}\). Then the equation becomes \(150^{\circ}+\angle1 = 180^{\circ}\). Subtract 150° from both sides: \(\angle1=180^{\circ}- 150^{\circ}=30^{\circ}\).

Answer:

30°