Question

Question was provided via image upload.

Explanation:

Step1: Set up the equation

From the segment addition postulate, we know that \( (x + 12)+(16 + x)=20 \).

Step2: Simplify the left side

Combine like terms: \( x + 12+16 + x = 2x+28 \). So the equation becomes \( 2x + 28=20 \).

Step3: Solve for x

Subtract 28 from both sides: \( 2x=20 - 28=- 8 \). Then divide both sides by 2: \( x=\frac{-8}{2}=-4 \).

Answer:

\( x = - 4 \)