Question

if m∠1 = 29° and m∠2 = 92°, what is m∠3? a. 63° b. 121° c. 59° d. 122° note: figure is not drawn to scale.

Explanation:

Step1: Recall triangle - angle sum property

The sum of the interior angles of a triangle is 180°. So, \(m\angle1 + m\angle2+m\angle3=180^{\circ}\).

Step2: Substitute given angle - measures

We know that \(m\angle1 = 29^{\circ}\) and \(m\angle2 = 92^{\circ}\). Substituting these values into the equation \(29^{\circ}+92^{\circ}+m\angle3 = 180^{\circ}\).

Step3: Solve for \(m\angle3\)

First, add 29 and 92: \(29 + 92=121\). Then the equation becomes \(121^{\circ}+m\angle3 = 180^{\circ}\). Subtract 121 from 180: \(m\angle3=180 - 121=59^{\circ}\).

Answer:

C. \(59^{\circ}\)