Question

In a drawing with parallel lines a and b and lines c and d, which angle is not necessarily congruent to angle 1?

a) <12
b) <9
c) <16
d) <3

Answer 1

In a drawing with parallel lines, angle 1 is not necessarily congruent to angle 3.

Step-by-step explanation:

In a drawing with parallel lines, angles formed by transversals are either congruent or supplementary.

Angle 1 and angle 12 are alternate interior angles, and since the lines are parallel, alternate interior angles are congruent. Therefore, angle 1 is necessarily congruent to angle 12.

Angle and angle 9 are corresponding angles, and corresponding angles are congruent when the lines are parallel. Therefore, angle 1 is necessarily congruent to angle 9.

Angle 1 and angle 16 are vertical angles, and vertical angles are always congruent. Therefore, angle 1 is necessarily congruent to angle 16.

Angle 1 and angle 3 are not located on parallel lines or formed by transversals. Therefore, angle 1 is not necessarily congruent to angle 3.