06/18/2020 (2011: National Target Round, Problem 1)

Q: In triangle ABC, m∠A = 60° and m∠B = 70°. The bisectors of ∠B and ∠C intersect at point D. What is the degree measure of ∠BDC?

A: 120°

When you have a problem like this (a geometry problem), always draw a diagram:

Because ABC is a triangle, that means that the sum of the angle measures is equal to 180 degrees, so m∠C = 180 - (60 + 70) = 180 - 130 = 50 degrees.

Because CD and BD bisect their respective angles, that means m∠BCD = 50/2 = 25 degrees and  m∠CBD = 70/2 = 35 degrees.

Because DBC is a triangle, that means that the sum of the angle measures is equal to 180 degrees, so m∠BDC = 180 - (25 + 35) = 180 - 60 = 120 degrees.