Question

Please solve questions number 12 please please

Answer 1

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❥ Given ∠AOE = 40° & ∠BOD = 35°

❥ Clearly ∠AOC = ∠BOD [Vertically opposite angles] 

❥ ⇒ ∠AOC = 35°

❥ ∠BOF = ∠AOE [Vertically opposite angles] 

❥ ⇒ ∠BOF = 40° 

❥ Now, ∠AOB = 180° [Straight angles] 

❥ ⇒ ∠AOC + ∠COF + ∠BOF = 180° [Angles sum property] 

❥ ⇒ 35° + ∠COF + 40° = 180°

❥ ⇒ ∠COF = 180° - 75° = 105°

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

❥ ∴ ∠DOE = 105°

Hopes it help you✌️✌️

Answer 2

EXPLANATION.

• GIVEN

<BOD = X

<AOE = 2X

<COF = 90°

To find <AOE and <AOC

<COF = <DOE = [ vertically opposite angles]

Therefore,

<COF = 90°

From the figure we know that AOB is straight

line

It will be written as =

<AOB = 180°

we can write as =

<AOE + <EOD + <BOD = 180°

2x + 90° + x = 180

3x = 90°

x = 30°

Therefore,

<AOE = 2X = 2 X 30° = 60°

<AOE = 60°

<BOD = X

<BOD = 30°

Hence,

<AOE = 60°

<AOC = <BOD [ vertically opposite angle]

<AOC = 30°

Therefore,

<AOE = 60° AND <AOC = 30°

Note = we can also see image statement.