Question

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

Explanation:

Step1: Recall supplementary angles sum to 180°

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

Step2: Solve for \( x \)

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

Step3: Find \( m\angle Q \)

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

Answer:

\( 123^\circ \)