Question

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

Explanation:

Step1: Recall supplementary angles property

Supplementary angles sum to \(180^\circ\), so \(m\angle P + m\angle Q = 180^\circ\).
Substitute \(m\angle P=(4x + 1)^\circ\) and \(m\angle Q=(9x - 3)^\circ\):
\((4x + 1)+(9x - 3)=180\)

Step2: Solve for \(x\)

Combine like terms:
\(4x+9x + 1-3 = 180\)
\(13x-2 = 180\)
Add 2 to both sides:
\(13x=180 + 2=182\)
Divide by 13:
\(x=\frac{182}{13}=14\)

Step3: Find \(m\angle Q\)

Substitute \(x = 14\) into \(m\angle Q=(9x - 3)^\circ\):
\(m\angle Q=9(14)-3=126 - 3 = 123^\circ\)

Answer:

\(123^\circ\)