Question

finding angles ∠a and ∠b are complementary. find m∠a and m∠b. 47. m∠a = 8x − 7 m∠b = x − 11

Explanation:

Step1: Recall complementary angles property

Complementary angles sum to \(90^\circ\), so \(m\angle A + m\angle B = 90^\circ\).
Substitute \(m\angle A = 8x - 7\) and \(m\angle B = x - 11\) into the equation:
\((8x - 7)+(x - 11)=90\)

Step2: Simplify and solve for \(x\)

Combine like terms: \(8x + x - 7 - 11 = 90\)
\(9x - 18 = 90\)
Add 18 to both sides: \(9x = 90 + 18\)
\(9x = 108\)
Divide by 9: \(x=\frac{108}{9}=12\)

Step3: Find \(m\angle A\)

Substitute \(x = 12\) into \(m\angle A = 8x - 7\):
\(m\angle A = 8(12)-7 = 96 - 7 = 89^\circ\)

Step4: Find \(m\angle B\)

Substitute \(x = 12\) into \(m\angle B = x - 11\):
\(m\angle B = 12 - 11 = 1^\circ\)

Answer:

\(m\angle A = 89^\circ\), \(m\angle B = 1^\circ\)