Question

determining angle measures
let ( mangle a = 40^{circ}). if (angle b) is a complement of (angle a), and (angle c) is a supplement of (angle b), find these measures
( mangle b=)
( mangle c=)

Explanation:

Step1: Find the measure of ∠B

Complementary angles sum to \(90^{\circ}\).
\(m\angle B=90^{\circ}-m\angle A\)
Substitute \(m\angle A = 40^{\circ}\) into the formula:
\(m\angle B=90^{\circ}- 40^{\circ}=50^{\circ}\)

Step2: Find the measure of ∠C

Supplementary angles sum to \(180^{\circ}\).
\(m\angle C=180^{\circ}-m\angle B\)
Substitute \(m\angle B = 50^{\circ}\) into the formula:
\(m\angle C=180^{\circ}-50^{\circ}=130^{\circ}\)

Answer:

\(m\angle B = 50^{\circ}\)
\(m\angle C = 130^{\circ}\)