Question

lesson 6 | session 2
name
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?
bd and 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 ∠cfg?
b. what is the measure of the angle you named in problem 1a?
2 what is the value of x? show your work.
3 describe a sequence of transformations
you can use to show ∠jlk ≅ ∠qnr.
vocabulary
alternate exterior
angles
when two lines are
cut by a transversal, a
pair of angles on
opposite sides of the
transversal and
outside the two lines.
alternate interior
angles
when two lines are
cut by a transversal,
a pair of angles on
opposite sides of
the transversal
and between the
two lines.
corresponding
angles
angles in the same
relative position when
two lines are cut by a
transversal.

Explanation:

Step1: Identify the relationship between angles

Since the two lines are parallel and cut by a transversal, \(4x^{\circ}\) and \(140^{\circ}\) are supplementary angles. So, \(4x + 140=180\).

Step2: Solve the equation for \(x\)

Subtract \(140\) from both sides of the equation:
\(4x=180 - 140\)
\(4x = 40\)
Divide both sides by \(4\):
\(x=\frac{40}{4}=10\)

Answer:

\(x = 10\)