Find X in Circle Sectors: Solving 3x+4 and 5x+16 Angle Relationship

To solve this problem, we'll follow these steps:

• Step 1: Apply the triangle angle sum property.
• Step 2: Combine like terms in the equation.
• Step 3: Solve the resulting linear equation for $x$.

Now, let's work through each step:
Step 1: Based on our assumption, the angles $3x + 4$ and $5x + 16$ should sum to 180 degrees. We write the equation:
$(3x + 4) + (5x + 16) = 180$.

Step 2: Combine like terms:
$3x + 5x + 4 + 16 = 180$.

Step 3: Simplify the equation:
$8x + 20 = 180$.

Subtract 20 from both sides:
$8x = 160$.

Finally, divide by 8 to solve for $x$:
$x = \frac{160}{8} = 20$.

Therefore, the solution to the problem is $x = 20$.