Question

solve for x

Explanation:

Step1: Apply exterior angle theorem

The exterior angle of a triangle equals the sum of the two non-adjacent interior angles. So:
$$48^\circ = (3x+1)^\circ + (2x+2)^\circ$$

Step2: Simplify the right-hand side

Combine like terms:
$$48 = 5x + 3$$

Step3: Isolate the variable term

Subtract 3 from both sides:
$$48 - 3 = 5x$$
$$45 = 5x$$

Step4: Solve for x

Divide both sides by 5:
$$x = \frac{45}{5}$$

Answer:

$x=9$