Question

finding angles ∠a and ∠b are complementary. find m∠a and m∠b. 9) m∠a = 5x + 8 m∠b = x + 4 10) m∠a = 3x − 7 m∠b = 11x − 1

Explanation:

Problem 9

Step1: Recall complementary angles sum to \(90^\circ\)

Since \(\angle A\) and \(\angle B\) are complementary, \(m\angle A + m\angle B = 90^\circ\). 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: \(6x + 12 = 90\)
Subtract 12 from both sides: \(6x = 90 - 12 = 78\)
Divide by 6: \(x = \frac{78}{6} = 13\)

Step3: Find \(m\angle A\) and \(m\angle B\)

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

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

Problem 10

Step1: Recall complementary angles sum to \(90^\circ\)

Since \(\angle A\) and \(\angle B\) are complementary, \(m\angle A + m\angle B = 90^\circ\). Substitute \(m\angle A = 3x - 7\) and \(m\angle B = 11x - 1\) into the equation:
\((3x - 7) + (11x - 1) = 90\)

Step2: Simplify and solve for \(x\)

Combine like terms: \(14x - 8 = 90\)
Add 8 to both sides: \(14x = 90 + 8 = 98\)
Divide by 14: \(x = \frac{98}{14} = 7\)

Step3: Find \(m\angle A\) and \(m\angle B\)

For \(m\angle A\): Substitute \(x = 7\) into \(3x - 7\):
\(3(7) - 7 = 21 - 7 = 14^\circ\)

For \(m\angle B\): Substitute \(x = 7\) into \(11x - 1\):
\(11(7) - 1 = 77 - 1 = 76^\circ\)

Answer:

s:

• Problem 9: \(m\angle A = 73^\circ\), \(m\angle B = 17^\circ\)
• Problem 10: \(m\angle A = 14^\circ\), \(m\angle B = 76^\circ\)