Question

1. there is a horizontal straight line with two arrows (left and right), and two oblique lines m and n intersecting it. the angle between line m and the horizontal line below is (3x^{circ}), and the angle between line n and the horizontal line above is ((2x + 20)^{circ}).

Explanation:

Step1: Identify supplementary angles

Since lines \(m\) and \(n\) are parallel, \(3x^\circ\) and \((2x+20)^\circ\) are same-side interior angles, so they are supplementary (sum to \(180^\circ\)).
$$3x + (2x + 20) = 180$$

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.
$$x = \frac{160}{5}$$

Answer:

\(x = 32\)