Question

finding angles ∠a and ∠b are supplementary. find m∠a and m∠b. 50. m∠a = 6x − 1 m∠b = 5x − 17

Explanation:

Step1: Recall supplementary angles property

Supplementary angles sum to \(180^\circ\), so \(m\angle A + m\angle B = 180^\circ\).
Substitute \(m\angle A = 6x - 1\) and \(m\angle B = 5x - 17\) into the equation:
\((6x - 1)+(5x - 17)=180\)

Step2: Simplify and solve for \(x\)

Combine like terms: \(6x + 5x - 1 - 17 = 180\)
\(11x - 18 = 180\)
Add 18 to both sides: \(11x = 180 + 18 = 198\)
Divide by 11: \(x=\frac{198}{11}=18\)

Step3: Find \(m\angle A\)

Substitute \(x = 18\) into \(m\angle A = 6x - 1\):
\(m\angle A = 6(18)-1 = 108 - 1 = 107^\circ\)

Step4: Find \(m\angle B\)

Substitute \(x = 18\) into \(m\angle B = 5x - 17\):
\(m\angle B = 5(18)-17 = 90 - 17 = 73^\circ\)

Answer:

\(m\angle A = 107^\circ\), \(m\angle B = 73^\circ\)