Question

∠f and ∠q are supplementary. what is the value of x? x =

Explanation:

Step1: Recall supplementary angles

Supplementary angles sum to \(180^\circ\). So, \(\angle F + \angle Q = 180^\circ\).
Substitute the given expressions: \((4x - 4) + (21x + 9) = 180\).

Step2: Combine like terms

Combine the \(x\)-terms and constant terms: \(4x + 21x - 4 + 9 = 180\)
Simplify: \(25x + 5 = 180\).

Step3: Solve for \(x\)

Subtract 5 from both sides: \(25x = 180 - 5\)
\(25x = 175\)
Divide both sides by 25: \(x = \frac{175}{25}\)
\(x = 7\).

Answer:

\(7\)