Question

a) an angle measures 57°. what is the measure of its complement? b) an angle measures 116°. what is the measure of its supplement?

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles add up to 90°. Let the given angle be $\theta = 57^{\circ}$. The measure of its complement $x$ is found by $x=90^{\circ}-\theta$.
$x = 90 - 57$

Step2: Calculate the complement

$x=33^{\circ}$

Step3: Recall the definition of supplementary angles

Supplementary angles add up to 180°. Let the given angle be $\alpha = 116^{\circ}$. The measure of its supplement $y$ is found by $y = 180^{\circ}-\alpha$.
$y=180 - 116$

Step4: Calculate the supplement

$y = 64^{\circ}$

Answer:

Measure of the complement: $33^{\circ}$
Measure of the supplement: $64^{\circ}$