Question

1. ∠p and ∠q are supplementary angles. if m∠p=(4x + 1)° and m∠q=(9x - 3)°, find m∠q.

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles sum to \(180^{\circ}\). So, \(m\angle P + m\angle Q=180^{\circ}\).
Substitute \(m\angle P=(4x + 1)^{\circ}\) and \(m\angle Q=(9x - 3)^{\circ}\) into the equation:
\((4x + 1)+(9x - 3)=180\)

Step2: Simplify the left - hand side of the equation

Combine like terms:
\(4x+9x+1 - 3=180\)
\(13x-2 = 180\)

Step3: Solve for \(x\)

Add \(2\) to both sides of the equation:
\(13x-2 + 2=180 + 2\)
\(13x=182\)
Divide both sides by \(13\):
\(x=\frac{182}{13}=14\)

Step4: Find \(m\angle Q\)

Substitute \(x = 14\) into the expression for \(m\angle Q=(9x - 3)^{\circ}\)
\(m\angle Q=(9\times14-3)^{\circ}\)
First, calculate \(9\times14 = 126\)
Then, \(126-3=123\)

Answer:

\(m\angle Q = 123^{\circ}\)