Question

(a) un ángulo mide 108°. ¿cuál es la medida de su suplemento? (b) un ángulo mide 27°. ¿cuál es la medida de su complemento? medida del suplemento: ° medida del complemento: °

Explanation:

Step1: Recall supplement - angle formula

The sum of an angle and its supplement is 180°. Let the given angle be $\theta = 108^{\circ}$, and its supplement be $x$. Then $\theta+x = 180^{\circ}$, so $x=180^{\circ}-\theta$.

Step2: Calculate the supplement

Substitute $\theta = 108^{\circ}$ into the formula: $x = 180^{\circ}-108^{\circ}=72^{\circ}$.

Step3: Recall complement - angle formula

The sum of an angle and its complement is 90°. Let the given angle be $\alpha = 27^{\circ}$, and its complement be $y$. Then $\alpha + y=90^{\circ}$, so $y = 90^{\circ}-\alpha$.

Step4: Calculate the complement

Substitute $\alpha=27^{\circ}$ into the formula: $y=90^{\circ}-27^{\circ}=63^{\circ}$.

Answer:

medida del suplemento: $72^{\circ}$
medida del complemento: $63^{\circ}$