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 by adding the measures of angles BDC and CDB, which gives 127°.

Step-by-step explanation:

To find the measure of angle ABC, we need to use the fact that the exterior angle of a triangle is equal to the sum of the two opposite interior angles. In triangle BCD, angle DBA (also called angle ABC) is an exterior angle, and angles BDC and CDB are the two opposite interior angles.

We are given that:

• Angle BDC = 67°
• Angle CDB = 60°

To find angle ABC, we add the measures of angle BDC and angle CDB:

Angle ABC = Angle BDC + Angle CDB

Angle ABC = 67° + 60°

Angle ABC = 127°

Therefore, the measure of angle ABC is 127 degrees.