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=square^{circ} )
( mangle c=square^{circ} )

Explanation:

Step1: Find \(m\angle B\)

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

Step2: Find \(m\angle C\)

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

Answer:

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