Question

finding angles ∠a and ∠b are supplementary. find m∠a and m∠b. 49. m∠a = 3x m∠b = x + 8

Explanation:

Step1: Recall supplementary angles property

Supplementary angles sum to \(180^\circ\), so \(m\angle A + m\angle B = 180^\circ\).
Substitute \(m\angle A = 3x\) and \(m\angle B = x + 8\) into the equation:
\(3x+(x + 8)=180\)

Step2: Simplify and solve for \(x\)

Combine like terms: \(4x+8 = 180\)
Subtract 8 from both sides: \(4x=180 - 8=172\)
Divide by 4: \(x=\frac{172}{4}=43\)

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

For \(m\angle A\): Substitute \(x = 43\) into \(3x\), so \(m\angle A=3\times43 = 129^\circ\)
For \(m\angle B\): Substitute \(x = 43\) into \(x + 8\), so \(m\angle B=43 + 8=51^\circ\)

Answer:

\(m\angle A = 129^\circ\), \(m\angle B = 51^\circ\)