Question

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

Answer 1

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