Question

finding angles ∠a and ∠b are complementary. find m∠a and m∠b. 45. m∠a = 5x + 8 m∠b = x + 4

Explanation:

Step1: Recall complementary angles property

Complementary angles sum to \(90^\circ\), so \(m\angle A + m\angle B = 90^\circ\).
Substitute \(m\angle A = 5x + 8\) and \(m\angle B = x + 4\) into the equation:
\((5x + 8)+(x + 4)=90\)

Step2: Simplify and solve for \(x\)

Combine like terms: \(5x + x + 8 + 4 = 90\)
\(6x + 12 = 90\)
Subtract 12 from both sides: \(6x = 90 - 12 = 78\)
Divide by 6: \(x=\frac{78}{6}=13\)

Step3: Find \(m\angle A\)

Substitute \(x = 13\) into \(m\angle A = 5x + 8\):
\(m\angle A = 5(13)+8 = 65 + 8 = 73^\circ\)

Step4: Find \(m\angle B\)

Substitute \(x = 13\) into \(m\angle B = x + 4\):
\(m\angle B = 13 + 4 = 17^\circ\)

Answer:

\(m\angle A = 73^\circ\), \(m\angle B = 17^\circ\)