Question

In triangle ABC, line CB extends through point D. Line BC extends to form an exterior angle that measures 135 degrees. Angle CAB measures 75 degrees. What is the measure of angle ABC?

1) 15°
2) 45°
3) 60°
4) 75°

Answer 1

In triangle ABC, angle ABC cannot be determined from the given information.

Step-by-step explanation:

In triangle ABC, angle CAB measures 75 degrees. The exterior angle of triangle ABC, formed by extending line BC, measures 135 degrees.

By the Exterior Angle Theorem, the measure of angle ABC is equal to the sum of angle CAB and the exterior angle of triangle ABC. Therefore, angle ABC = 75 degrees + 135 degrees = 210 degrees.

However, the sum of the angles in a triangle is always 180 degrees. Therefore, the measure of angle ABC cannot be 210 degrees.

The correct answer is not provided in the given options.