Question

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 \( 90^\circ \))

Since \( \angle B \) is a complement of \( \angle A \), we use the formula \( m\angle A + m\angle B = 90^\circ \). Given \( m\angle A = 40^\circ \), we substitute:
\( 40^\circ + m\angle B = 90^\circ \)
Subtract \( 40^\circ \) from both sides:
\( m\angle B = 90^\circ - 40^\circ = 50^\circ \)

Step2: Find \( m\angle C \) (supplementary angles sum to \( 180^\circ \))

Since \( \angle C \) is a supplement of \( \angle B \), we use the formula \( m\angle B + m\angle C = 180^\circ \). We know \( m\angle B = 50^\circ \), so substitute:
\( 50^\circ + m\angle C = 180^\circ \)
Subtract \( 50^\circ \) from both sides:
\( m\angle C = 180^\circ - 50^\circ = 130^\circ \)

Answer:

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