Question

find (a) the complement and (b) the supplement of an angle with the measure 19°15
(a) the complement of 19°15 is □°□. (simplify your answer.)
(b) the supplement of 19°15 is □°□. (simplify your answer.)

Explanation:

Step1: Recall complement and supplement definitions

Complementary angles sum to \(90^\circ\), supplementary to \(180^\circ\). \(1^\circ = 60'\).

Step2: Solve part (a) - Complement

Subtract \(19^\circ15'\) from \(90^\circ\).
\(90^\circ = 89^\circ60'\) (convert to same units).
\(89^\circ60' - 19^\circ15' = (89 - 19)^\circ + (60 - 15)' = 70^\circ45'\).

Step3: Solve part (b) - Supplement

Subtract \(19^\circ15'\) from \(180^\circ\).
\(180^\circ = 179^\circ60'\).
\(179^\circ60' - 19^\circ15' = (179 - 19)^\circ + (60 - 15)' = 160^\circ45'\).

Answer:

(a) \(70^\circ45'\)
(b) \(160^\circ45'\)