Question

name: redacted date: directions: find all missing angle 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 three angles of the triangle be \(A = 76^{\circ}\), \(B=59^{\circ}\), and \(C = m\angle1\). So, \(A + B + C=180^{\circ}\).

Step2: Substitute the known angles and solve for \(m\angle1\)

We have \(76^{\circ}+59^{\circ}+m\angle1 = 180^{\circ}\). First, add 76 and 59: \(76 + 59=135\). Then the equation becomes \(135^{\circ}+m\angle1 = 180^{\circ}\). Subtract 135 from 180: \(m\angle1=180^{\circ}- 135^{\circ}=45^{\circ}\).

Answer:

\(45^{\circ}\)