Question

4
note: figure is not drawn to scale.
if ( mangle1 = 29^{circ} ) and ( mangle2 = 92^{circ} ), what is ( mangle3 )?
a. ( 59^{circ} )
b. ( 121^{circ} )
c. ( 63^{circ} )
d. ( 122^{circ} )

Explanation:

Step1: Recall the triangle angle - sum property

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

Step2: Solve for \(m\angle3\)

We know \(m\angle1 = 29^{\circ}\) and \(m\angle2 = 92^{\circ}\). Substitute these values into the equation:
\(m\angle3=180^{\circ}-(m\angle1 + m\angle2)\)
\(m\angle3=180^{\circ}-(29^{\circ}+92^{\circ})\)
First, calculate \(29^{\circ}+92^{\circ}=121^{\circ}\).
Then, \(m\angle3 = 180^{\circ}-121^{\circ}=59^{\circ}\)

Answer:

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