Question

in △abc, m∠a = 75° and m∠c = 20°, what is m∠b?
a. 55°
b. 85°
c. 95°
d. 265°

Explanation:

Step1: Recall angle - sum property of a triangle

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

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

We can rewrite the formula as \(m\angle B=180^{\circ}-m\angle A - m\angle C\). Substitute \(m\angle A = 75^{\circ}\) and \(m\angle C = 20^{\circ}\) into the formula: \(m\angle B=180^{\circ}-75^{\circ}-20^{\circ}\).
\(m\angle B = 85^{\circ}\).

Answer:

B. \(85^{\circ}\)