Line DB bisects ∠ABC, m∠ABD = 4x, and m∠DBC = x + 36. Find m∠ABC. Choose True or False for each statement.

A. m∠ABC = 48° A. TRUE B. FALSE

B. m∠ABC = 96° A. TRUE B. FALSE

C. m∠DBC = 48° A. TRUE B. FALSE

Since DB bisects ∠ABC and ∠ABC = ∠ABD + ∠DBC, then

∠ABD = ∠DBC, that is

4x = x + 36 (subtract x from both sides)

3x = 36 (divide both sides by 3)

x = 12

∠ABD = 4x = 4 * 12 = 48°

∠DBC = x + 36 = 12 + 36 = 48°

∠ABC = 48° + 48° = 96°

Thus statement A is FALSE

statement B is TRUE

statement C is TRUE