Question

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

Explanation:

Step1: Use supplementary - angle property

Since $\angle P$ and $\angle Q$ are supplementary, $m\angle P + m\angle Q=180^{\circ}$. So, $(4x + 1)+(9x - 3)=180$.

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 $m\angle Q$. $m\angle Q=(9x - 3)^{\circ}=(9\times14-3)^{\circ}=(126 - 3)^{\circ}=123^{\circ}$.

Answer:

$123^{\circ}$