Question

use this figure to answer the questions below.
what is the value of x?

Explanation:

Step1: Set up the equation

Since \(4x + 3\) and \(4x + 9\) are supplementary angles (they form a linear pair), their sum is \(180^{\circ}\). So, \((4x + 3)+(4x + 9)=180\).

Step2: Simplify the equation

Combine like - terms: \(4x+4x + 3 + 9=180\), which simplifies to \(8x+12 = 180\).

Step3: Solve for \(x\)

Subtract \(12\) from both sides: \(8x=180 - 12\), so \(8x=168\). Then divide both sides by \(8\): \(x=\frac{168}{8}=21\).

Answer:

\(21\)