Question

find (a) the complement and (b) the supplement of an angle with the measure 17°16′. (a) the complement of 17°16′ is □°□′. (simplify your answer.)

Explanation:

Step1: Recall complement formula

The complement of an angle \( \theta \) is \( 90^\circ - \theta \). Here, \( \theta = 17^\circ 16' \). First, convert \( 90^\circ \) to \( 89^\circ 60' \) (since \( 1^\circ = 60' \)).

Step2: Subtract the angle

Subtract \( 17^\circ 16' \) from \( 89^\circ 60' \).

• Degrees: \( 89 - 17 = 72 \)
• Minutes: \( 60 - 16 = 44 \)

So, \( 89^\circ 60' - 17^\circ 16' = 72^\circ 44' \).

Answer:

\( 72^\circ 44' \)