Question

persevere with problems find the measure of angle a and angle b for the given situation. complementary angles a and b, where ( mangle a = (y - 16)^circ ) and ( mangle b = (y + 4)^circ ) ( mangle a = ) 35 ( mangle b = ) 55

Explanation:

Step1: Recall complementary angles sum

Complementary angles sum to \(90^\circ\), so \(m\angle A + m\angle B = 90^\circ\).
Substitute \(m\angle A=(y - 16)^\circ\) and \(m\angle B=(y + 4)^\circ\):
\((y - 16)+(y + 4)=90\)

Step2: Solve for y

Simplify left side: \(y - 16 + y + 4 = 90\)
\(2y - 12 = 90\)
Add 12 to both sides: \(2y = 90 + 12 = 102\)
Divide by 2: \(y=\frac{102}{2}=51\)

Step3: Find \(m\angle A\)

Substitute \(y = 51\) into \(m\angle A=(y - 16)^\circ\):
\(m\angle A=(51 - 16)^\circ = 35^\circ\)

Step4: Find \(m\angle B\)

Substitute \(y = 51\) into \(m\angle B=(y + 4)^\circ\):
\(m\angle B=(51 + 4)^\circ = 55^\circ\)

Answer:

\(m\angle A = 35^\circ\), \(m\angle B = 55^\circ\)