Question

finding angles ∠a and ∠b are complementary. find ( mangle a ) and ( mangle b ).

1. ( mangle a = 3x - 7 )

( mangle b = 11x - 1 )

Explanation:

Step1: Recall complementary angles property

Complementary angles sum to \(90^\circ\), so \(m\angle A + m\angle B = 90^\circ\).
Substitute \(m\angle A = 3x - 7\) and \(m\angle B = 11x - 1\) into the equation:
\((3x - 7)+(11x - 1)=90\)

Step2: Simplify and solve for \(x\)

Combine like terms: \(3x + 11x - 7 - 1 = 90\)
\(14x - 8 = 90\)
Add 8 to both sides: \(14x = 90 + 8 = 98\)
Divide by 14: \(x=\frac{98}{14}=7\)

Step3: Find \(m\angle A\)

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

Step4: Find \(m\angle B\)

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

Answer:

\(m\angle A = 14^\circ\), \(m\angle B = 76^\circ\)