Question

(a) an angle measures 49°. what is the measure of its complement? (b) an angle measures 42°. what is the measure of its supplement? measure of the complement: ☐° measure of the supplement: ☐°

Explanation:

Part (a)

Step1: Recall complement definition

Complementary angles sum to \(90^\circ\). Let \(x\) be the complement. So, \(49^\circ + x = 90^\circ\).

Step2: Solve for \(x\)

Subtract \(49^\circ\) from both sides: \(x = 90^\circ - 49^\circ = 41^\circ\).

Part (b)

Step1: Recall supplement definition

Supplementary angles sum to \(180^\circ\). Let \(y\) be the supplement. So, \(42^\circ + y = 180^\circ\).

Step2: Solve for \(y\)

Subtract \(42^\circ\) from both sides: \(y = 180^\circ - 42^\circ = 138^\circ\).

Answer:

measure of the complement: \(41^\circ\)
measure of the supplement: \(138^\circ\)