Question

(a) an angle measures 57°. what is the measure of its complement? (b) an angle measures 51°. what is the measure of its supplement?
measure of the complement: \boxed{}^circ
measure of the supplement: \boxed{}^circ

Explanation:

Part (a)

Step1: Recall complement definition

Complementary angles sum to \(90^\circ\). Let \(x\) be the complement. So, \(57^\circ + x = 90^\circ\).

Step2: Solve for \(x\)

Subtract \(57^\circ\) from both sides: \(x = 90^\circ - 57^\circ = 33^\circ\).

Part (b)

Step1: Recall supplement definition

Supplementary angles sum to \(180^\circ\). Let \(y\) be the supplement. So, \(51^\circ + y = 180^\circ\).

Step2: Solve for \(y\)

Subtract \(51^\circ\) from both sides: \(y = 180^\circ - 51^\circ = 129^\circ\).

Answer:

measure of the complement: \(33^\circ\)
measure of the supplement: \(129^\circ\)