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: Recall the definition of complementary angles

Complementary angles add up to 90°. Given \(m\angle A = 40^{\circ}\), and \(\angle B\) is the complement of \(\angle A\). So \(m\angle B=90^{\circ}-m\angle A\).
\[m\angle B = 90 - 40=50^{\circ}\]

Step2: Recall the definition of supplementary angles

Supplementary angles add up to 180°. Since \(\angle C\) is the supplement of \(\angle B\) and \(m\angle B = 50^{\circ}\), then \(m\angle C=180^{\circ}-m\angle B\).
\[m\angle C=180 - 50 = 130^{\circ}\]

Answer:

\(m\angle B = 50\), \(m\angle C=130\)