Question

the complement of an angle whose measure is 59° is
a) 121°.
b) 149°.
c) 31°.
d) 59°.

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles are two angles whose sum is \( 90^\circ \). So, if we let the angle be \( \theta \) and its complement be \( \alpha \), then \( \theta+\alpha = 90^\circ \).

Step2: Substitute the given angle into the formula

We are given that \( \theta=59^\circ \). We need to find \( \alpha \). From the formula \( \theta+\alpha = 90^\circ \), we can solve for \( \alpha \) by rearranging the formula as \( \alpha=90^\circ - \theta \).
Substituting \( \theta = 59^\circ \) into the formula, we get \( \alpha=90^\circ- 59^\circ \).

Step3: Calculate the result

\( 90 - 59=31 \), so \( \alpha = 31^\circ \).

Answer:

C) \( 31^\circ \)