Question

practice describing congruent angle relationships

study the example showing how to use angle relationships to find unknown angle measures. then solve problems 1 - 6.

example
what is the value of x?
\\(\overline{bd}\\) and \\(\overline{eg}\\) are parallel, so corresponding angles are congruent.
\\(25x - 2=148\\)
\\(25x = 150\\)
\\(x = 6\\)
1 a. in the example, what angle forms a pair of alternate interior angles with \\(\angle cfg\\)?
b. what is the measure of the angle you named in problem 1a?
2 what is the value of x? show your work.
solution

Explanation:

Step1: Identify alternate - interior angles

For two parallel lines cut by a transversal, alternate - interior angles are non - adjacent angles between the two parallel lines and on opposite sides of the transversal. In the given example, $\angle BCF$ forms a pair of alternate interior angles with $\angle CFG$.

Step2: Find the measure of $\angle BCF$

Since $\angle CFG = 148^{\circ}$ and alternate - interior angles are congruent when the lines are parallel, the measure of $\angle BCF$ is also $148^{\circ}$.

Step3: Solve for $x$ in problem 2

The two angles $4x^{\circ}$ and $140^{\circ}$ are supplementary (because they are same - side interior angles for two parallel lines cut by a transversal, and same - side interior angles are supplementary). So, $4x+140 = 180$.

Step4: Isolate $x$

Subtract 140 from both sides of the equation: $4x=180 - 140$, so $4x = 40$. Then divide both sides by 4: $x=\frac{40}{4}=10$.

Answer:

1.
a. $\angle BCF$
b. $148^{\circ}$

1. $x = 10$