Question

finding angles ∠a and ∠b are supplementary. find m∠a and m∠b. 51. m∠a = 12x + 1 m∠b = x + 10

Explanation:

Step1: Recall supplementary angles property

Supplementary angles sum to \(180^\circ\), so \(m\angle A + m\angle B = 180^\circ\).
Substitute \(m\angle A = 12x + 1\) and \(m\angle B = x + 10\) into the equation:
\((12x + 1)+(x + 10)=180\)

Step2: Simplify and solve for \(x\)

Combine like terms: \(12x + x + 1 + 10 = 180\)
\(13x + 11 = 180\)
Subtract 11 from both sides: \(13x = 180 - 11 = 169\)
Divide by 13: \(x=\frac{169}{13}=13\)

Step3: Find \(m\angle A\)

Substitute \(x = 13\) into \(m\angle A = 12x + 1\):
\(m\angle A = 12(13)+1 = 156 + 1 = 157^\circ\)

Step4: Find \(m\angle B\)

Substitute \(x = 13\) into \(m\angle B = x + 10\):
\(m\angle B = 13 + 10 = 23^\circ\)

Answer:

\(m\angle A = 157^\circ\), \(m\angle B = 23^\circ\)