In the given figure, three lines AB, CD and EF intersect at a point O such that ∠AOE = 35° and ∠BOD = 40°.
Question:
In the given figure, three lines AB, CD and EF intersect at a point O such that ∠AOE = 35° and ∠BOD = 40°. Find the measure of ∠AOC, ∠BOF, ∠COF and ∠DOE.
Solution:
In the given figure,
∠AOC = ∠BOD = 40º (Vertically opposite angles)
∠BOF = ∠AOE = 35º (Vertically opposite angles)
Now, ∠EOC and ∠COF form a linear pair.
∴ ∠EOC + ∠COF = 180º
⇒ (∠AOE + ∠AOC) + ∠COF = 180º
⇒ 35º + 40º + ∠COF = 180º
⇒ 75º + ∠COF = 180º
⇒ ∠COF = 180º − 75º = 105º
Also, ∠DOE = ∠COF = 105º (Vertically opposite angles)
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.