Question

1. in the figure shown, lines f and g are parallel. select the angle that is congruent to angle 1.

a angle 2
b. angle 6
c angle 7
d. angle 8

Explanation:

Step1: Identify vertical angles and parallel - line relationships

Vertical angles are congruent. Also, when two parallel lines are cut by a transversal, corresponding angles and alternate - exterior/alternate - interior angles are congruent.
Angle \(1\) and angle \(3\) are vertical angles (\(\angle1\cong\angle3\)). Since lines \(f\) and \(g\) are parallel and cut by a transversal, \(\angle3\) and \(\angle7\) are alternate - exterior angles.
By the Alternate - Exterior Angles Theorem (if two parallel lines are cut by a transversal, then alternate - exterior angles are congruent), \(\angle3\cong\angle7\).
By the transitive property of congruence (\(a\cong b\) and \(b\cong c\) implies \(a\cong c\)), since \(\angle1\cong\angle3\) and \(\angle3\cong\angle7\), we have \(\angle1\cong\angle7\).

Step2: Check other options

• For option A: \(\angle1\) and \(\angle2\) are supplementary (\(\angle1+\angle2 = 180^{\circ}\)) because they form a linear pair. So \(\angle1

ot\cong\angle2\).

• For option B: \(\angle1\) and \(\angle6\): \(\angle1\) and \(\angle3\) are vertical angles (\(\angle1\cong\angle3\)), and \(\angle3\) and \(\angle5\) are supplementary (linear pair), \(\angle5\) and \(\angle6\) are vertical angles (\(\angle5\cong\angle6\)). So \(\angle1

ot\cong\angle6\).

• For option D: \(\angle1\) and \(\angle8\): \(\angle1\cong\angle3\), \(\angle3\) and \(\angle4\) are supplementary (linear pair), \(\angle4\cong\angle8\) (vertical angles). So \(\angle1

ot\cong\angle8\).

Answer:

C. Angle 7