Angles: Difficult Problems with Solutions

By Catalin David
Problem 1
∠ABC and ∠DBC are adjacent. ∠ABC has a measure of 53° and ∠DBC has a measure of 29°. The measure of ∠ABD is
Problem 2
∠ABC and ∠DBC are adjacent. ∠DBC has a measure of 85° and ∠ABD has a measure of 127°. The measure of ∠ABC is:
Problem 3
AC is the bisector of ∠BAD. If ∠BAC has a measure of 52°, then ∠BAD has a measure of .


Problem 4
∠AOB and ∠BOC are adjacent and complementary.
If ∠AOB = x°+8° and ∠BOC = 2x° - 17°, what is the measure of ∠AOB?


Problem 5
∠AOB and ∠BOC are adjacent and supplementary. If OE is the bisector of ∠BOC and m∠EOC = 30°, what is the measure of ∠AOB?


Problem 6
If lines a and b are parallel, lines c and d are also parallel and m∠13 = 40°, what is the measure of ∠2?


Problem 7
Point O is the intersection of lines AB and CD. If ∠AOC has a measure of x° and ∠BOC has a measure of 4x°, what is the measure of ∠AOD?


Problem 8
Point O is the intersection of AB and CD. If m∠BOC = x° and
m∠AOC = x° + 20°, what is the measure of ∠BOD?


Problem 9
∠AOB, ∠BOC, ∠COD are adjacent and supplementary. If ∠BOC has 80°, what is the measure of ∠AOB?


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