Question

current skill
what is the value of x?
40
find the measure of angle 2.
label optional

Explanation:

Step1: Identify congruent angles

The two vertical lines are parallel, so corresponding angles $\angle 7$ and $\angle 1$ are congruent. $\angle 1$ is supplementary to $\angle 2$, and $\angle 7$ is equal to $x+18$, while $\angle 2$ is equal to $3x+2$. Since $\angle 1 + \angle 2 = 180^\circ$ and $\angle 1 = \angle 7 = x+18$, we get:
$$x+18 + 3x+2 = 180$$

Step2: Combine like terms

Add the variable terms and constants:
$$4x + 20 = 180$$

Step3: Isolate the variable term

Subtract 20 from both sides:
$$4x = 180 - 20 = 160$$

Step4: Solve for x

Divide both sides by 4:
$$x = \frac{160}{4} = 40$$

Step5: Calculate measure of $\angle 2$

Substitute $x=40$ into $3x+2$:
$$3(40) + 2 = 120 + 2 = 122$$

Answer:

Value of $x$: $40$
Measure of angle 2: $122^\circ$