Geometric Proof

Question

Given: Ray BD bisects < ABC; <1 (<ABD) and <2 (<CBD) are complementary. Prove: m<2 = 45

Answer 1

Since BD bisects ∠ABC, ∠ABD = ∠CBD

 

Since ∠ABD and ∠CBD are complementary, ∠ABD + ∠CBD = 90°

 

By substitution, ∠CBD + ∠CBD = 90°

 

                                  2(∠CBD) = 90°

 

                                     ∠CBD = 45°