Question

(a) an angle measures 44°. what is the measure of its complement? (b) an angle measures 54°. what is the measure of its supplement? measure of the complement: measure of the supplement:

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles add up to 90°. Let the given angle be $\theta = 44^{\circ}$. The measure of its complement $x$ is found by the equation $x+44^{\circ}=90^{\circ}$.

Step2: Solve for the complement

$x = 90^{\circ}-44^{\circ}=46^{\circ}$

Step3: Recall the definition of supplementary angles

Supplementary angles add up to 180°. Let the given angle be $\alpha = 54^{\circ}$. The measure of its supplement $y$ is found by the equation $y + 54^{\circ}=180^{\circ}$.

Step4: Solve for the supplement

$y=180^{\circ}-54^{\circ}=126^{\circ}$

Answer:

measure of the complement: $46^{\circ}$
measure of the supplement: $126^{\circ}$