Question

solve for x. options: 20, 23, 32, -20

Explanation:

Step1: Identify supplementary angles

The angles $2x^\circ$ and $(3x+20)^\circ$ are same-side interior angles, which are supplementary (sum to $180^\circ$).
$$2x + (3x + 20) = 180$$

Step2: Combine like terms

Simplify the left side of the equation.
$$5x + 20 = 180$$

Step3: Isolate the variable term

Subtract 20 from both sides.
$$5x = 180 - 20$$
$$5x = 160$$

Step4: Solve for x

Divide both sides by 5.
$$x = \frac{160}{5}$$
$$x = 32$$

Answer:

32