Question

question 5 (multiple choice worth 3 points)
(interior and exterior angles lc)
for △abc, m∠a = 41.3° and m∠b = 103.4°. determine m∠c.
144.7°
72.38°
84.7°
35.3°

Explanation:

Step1: Recall the sum of angles in a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(m\angle A + m\angle B + m\angle C=180^{\circ}\).

Step2: Solve for \(m\angle C\)

We know \(m\angle A = 41.3^{\circ}\) and \(m\angle B = 103.4^{\circ}\). Substitute these values into the equation:
\(m\angle C=180^{\circ}-(m\angle A + m\angle B)\)
\(m\angle C = 180^{\circ}-(41.3^{\circ}+ 103.4^{\circ})\)
First, calculate the sum inside the parentheses: \(41.3^{\circ}+103.4^{\circ}=144.7^{\circ}\)
Then, \(m\angle C=180^{\circ}-144.7^{\circ}=35.3^{\circ}\)

Answer:

\(35.3^{\circ}\)