Question

AB and CD are straight line segments.
∠ AOE = 42° and ∠ DOB = 110°.
Find the values of the following angles giving a reason for each answer in the comment box.

The diagram is not drawn accurately.
i) obtuse ∠ AOC
ii) acute ∠ BOC
iii) acute ∠ DOE

Answer 1

i) To find the measurement of ∠AOC, we first need to find the measure of ∠EOD.

∠EOD = 180°-(∠AOE+∠DOB) [Supplimentary Angles]

∠EOD = 180°-(42°+110°)

∠EOD = 180°-152°

∠EOD = 28°

Now that we know the measurement of ∠AOE and ∠EOD, we can find the measure of ∠AOC

∠AOC = 180°-(∠AOE+∠EOD) [Supplimentary Angles]

∠AOC = 180°-(42°+28°)

∠AOC = 180°- 70°

∠AOC = 110°

ii) ∠BOC = ∠DOE + ∠EOA [Vertically Opposite angle]

∠BOC = ∠28° + ∠42°

∠BOC = 70°

iii) ∠DOE = 180°-(∠AOE+∠DOB) [Supplimentary Angles]

= 180°-(∠AOE+∠DOB) [Supplimentary Angles] ∠DOE = 180°-(42°+110°)

= 180°-(42°+110°)∠DOE = 180°-152°

= 180°-152°∠DOE = 28°