In figure, lines AB, CD and EF intersect at O. Find the measures of �

1.	In figure, lines AB, CD and EF intersect at O. Find the measures of ∠AOC, ∠DOE and ∠BOF
Answer» Given ∠AOE = 40⁰ & ∠BOD = 35⁰ Clearly ∠AOC = ∠BOD [Vertically opposite angles] ⇒ ∠AOC = 35⁰ Ans. ∠BOF = ∠AOE [Vertically opposite angles] ⇒ ∠BOF = 40⁰ Ans. Now, ∠AOB = 180⁰ [Straight angles] ⇒ ∠AOC + ∠COF + ∠BOF = 180⁰ [Angles sum property] ⇒ 35⁰ + ∠COF + 40⁰ = 180⁰ ⇒ ∠COF = 180⁰ - 75⁰ = 105⁰ Now, ∠DOE = ∠COF [Vertically opposite angles] ∴ ∠DOE = 105⁰

In figure, lines AB, CD and EF intersect at O. Find the measures of ∠AOC, ∠DOE and ∠BOF

Answer»

Given ∠AOE = 40⁰ & ∠BOD = 35⁰

Clearly ∠AOC = ∠BOD [Vertically opposite angles]

⇒ ∠AOC = 35⁰ Ans.

∠BOF = ∠AOE [Vertically opposite angles]

⇒ ∠BOF = 40⁰ Ans.

Now, ∠AOB = 180⁰ [Straight angles]

⇒ ∠AOC + ∠COF + ∠BOF = 180⁰ [Angles sum property]

⇒ 35⁰ + ∠COF + 40⁰ = 180⁰

⇒ ∠COF = 180⁰ - 75⁰ = 105⁰

Now, ∠DOE = ∠COF [Vertically opposite angles]

∴ ∠DOE = 105⁰