Question

In triangle b c d, line d b extends through point a to form exterior angle a b c. Angle b d c is 67 degrees and angle c d b is 60 degrees. What is the measure of angle abc?

1) 60°
2) 67°
3) 120°
4) 127°

Answer 1

The measure of angle ABC is found using the exterior angle theorem, which states the exterior angle is equal to the sum of the two opposite interior angles. Angle ABC is 67 degrees plus 60 degrees, which equals 127 degrees.

Step-by-step explanation:

To find the measure of angle ABC in triangle BCD with exterior angle ABC, we need to understand the exterior angle theorem. This theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. In this case, angle BDC is 67 degrees and angle CDB is 60 degrees.

According to the exterior angle theorem, angle ABC is equal to angle BDC plus angle CDB:

• Angle ABC = Angle BDC + Angle CDB
• Angle ABC = 67 degrees + 60 degrees
• Angle ABC = 127 degrees

Therefore, the measure of angle ABC is 127 degrees. The correct answer is option 4).