Question

Triangle B C D is shown. 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 m∠ABC?

m∠ABC = 60°
m∠ABC = 67°
m∠ABC = 120°
m∠ABC = 127°

Answer 1

To find \( m∠ABC \), we can use the exterior angle theorem which states that the measure of an exterior angle is equal to the sum of the measures of the two non-adjacent interior angles. In this case, angle \( ABC \) is the exterior angle at point A, and it can be calculated using the angles \( BDC \) and \( CDB \).

We are given:
- \( m∠BDC = 67° \)
- \( m∠CDB = 60° \)

According to the exterior angle theorem:

\[
m∠ABC = m∠BDC + m∠CDB
\]

Substituting in the values we have:

\[
m∠ABC = 67° + 60° = 127°
\]

Thus, the measure of angle \( ABC \) is:

\[
\boxed{127°}
\]