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 { b d } \\) and \\( \overline { e g } \\) are parallel, so corresponding angles are congruent.
\\( 25 x - 2 = 148 \\)
\\( 25 x = 150 \\)
\\( x = 6 \\)
1 a. in the example, what angle forms a pair of alternate interior angles with \\( \angle c f g \\) ?
b. what is the measure of the angle you named in problem 1a?

Explanation:

Step1: Identify alternate - interior angles

Alternate - interior angles are formed when a transversal intersects two parallel lines. The transversal is \(AH\), and the parallel lines are \(BD\) and \(EG\). For \(\angle CFG\), the alternate - interior angle is \(\angle BCF\).

Step2: Use the relationship in the example

Since \(BD\parallel EG\) and \(AH\) is the transversal, alternate - interior angles are congruent. In the example, we know that \(\angle CFG = 148^{\circ}\). Because \(\angle BCF\) and \(\angle CFG\) are alternate - interior angles, \(\angle BCF=\angle CFG\)

Answer:

a. \(\angle BCF\)
b. \(148^{\circ}\)