Question

diagram shows two intersecting lines (one horizontal, one slanted) forming angles: $(3x + 19)^circ$ and $101^circ$ (adjacent on a straight line).

Explanation:

Step1: Identify supplementary angles

The two angles \((3x + 19)^\circ\) and \(101^\circ\) are supplementary, so their sum is \(180^\circ\).
\[
(3x + 19) + 101 = 180
\]

Step2: Simplify the equation

Combine like terms:
\[
3x + 120 = 180
\]

Step3: Solve for \(x\)

Subtract 120 from both sides:
\[
3x = 180 - 120
\]
\[
3x = 60
\]
Divide both sides by 3:
\[
x = \frac{60}{3}
\]
\[
x = 20
\]

Answer:

\(x = 20\)