Question

1. given

△abc
with angles
∠a = 40° & ∠b = 70°,
what is the measure of
∠c?
50°
70°
80°
60°

Explanation:

Step1: Recall the sum of angles in a triangle

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

Step2: Substitute the given values

We know \(\angle A = 40^{\circ}\) and \(\angle B=70^{\circ}\). Substituting into the formula: \(40^{\circ}+70^{\circ}+\angle C=180^{\circ}\).

Step3: Solve for \(\angle C\)

First, calculate \(40 + 70=110\). Then, \(\angle C=180^{\circ}-(40^{\circ}+70^{\circ})=180^{\circ}-110^{\circ}=70^{\circ}\).

Answer:

\(70^{\circ}\) (the second option)