Question

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

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to 180°. So, \(m\angle P + m\angle Q=180^{\circ}\).
Substitute the given expressions: \((4x + 1)+(9x - 3)=180\).

Step2: Simplify the left - hand side

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

Step3: Solve for \(x\)

Add 2 to both sides: \(13x=180 + 2=182\).
Then divide both sides by 13: \(x=\frac{182}{13}=14\).

Step4: Find \(m\angle Q\)

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

Answer:

\(123^{\circ}\)