Question

∠a and ∠b are supplementary. if m∠a = 6x + 17 and m∠b = 3x + 10, find m∠a. after you enter your answer press go. m∠a =

Explanation:

Step1: Use the property of supplementary angles

Since \(\angle A\) and \(\angle B\) are supplementary, \(m\angle A + m\angle B=180^{\circ}\).
Substitute \(m\angle A = 6x + 17\) and \(m\angle B = 3x + 10\) into the equation:
\((6x + 17)+(3x + 10)=180\)

Step2: Simplify the equation

Combine like - terms:
\(6x+3x+17 + 10=180\)
\(9x+27 = 180\)

Step3: Solve for \(x\)

Subtract 27 from both sides:
\(9x=180 - 27\)
\(9x=153\)
Divide both sides by 9:
\(x=\frac{153}{9}=17\)

Step4: Find \(m\angle A\)

Substitute \(x = 17\) into \(m\angle A=6x + 17\):
\(m\angle A=6\times17+17\)
\(m\angle A = 102+17\)
\(m\angle A=119\)

Answer:

\(119\)