Question

if triangle abc has a 130° angle at vertex b, which statement must be true?

m∠a = 15° and m∠c = 35°

m∠a + m∠b = 18

m∠a = 20° and m∠c = 20°

m∠a + m∠c = 50

Explanation:

Step1: Recall the angle - sum property of a triangle

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

Step2: Substitute \(m\angle B = 130^{\circ}\) into the angle - sum formula

We get \(m\angle A + 130^{\circ}+m\angle C=180^{\circ}\).

Step3: Solve for \(m\angle A + m\angle C\)

Subtract \(130^{\circ}\) from both sides of the equation \(m\angle A + m\angle C+130^{\circ}=180^{\circ}\).

$$m\angle A + m\angle C=180^{\circ}- 130^{\circ}=50^{\circ}$$

Answer:

\(m\angle A + m\angle C = 50^{\circ}\)