Question

NEED HELP

⬆️Refer the attachment⬆️


❌No irrelevant answers❌​

Answer 1

⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⋆ ANSWER ⋆

GIVEN : • AB , CD & EF are lines and all intersect at O

• ∠AOC =30° & ∠BOF = 35°

REQUIRED TO FIND : AOE , EOD, BOD & COF

⠀ ⠀ ⠀⠀ ⠀⠀ ⋆ SOLUTION ⋆

FOR ∠AOE ,

➠ here we know that CD , AB & EF intersect each other

so , ∠AOE = ∠FOB ( vertically opposite angle)

( vertically opposite angle) ∴ ∠AOE = 30°

━━━━━━━━━━━━━━━━━━━━

FOR ∠EOD,

➠ here we know that CD is a line

so , ∠COE + ∠EOD = 180° ( angle on a straight line)

[ ∠COE = ∠COA + ∠AOE ]

[∠COA + ∠AOE ] + ∠EOD = 180°

30° + 35° + ∠EOD = 180°

65° + ∠EOD = 180°

∠EOD = 180° - 65°

∴∠EOD = 115°

━━━━━━━━━━━━━━━━━━━━

for ∠BOD ,

➠ here we know that CD , AB & EF intersect each other

so , ∠BOD = ∠AOC ( vertically opposite angle)

∴ ∠BOD = 35°

━━━━━━━━━━━━━━━━━━━━

for ∠COF ,

➠ here we know that CD , AB & EF intersect each other

so , ∠COF = ∠EOD ( vertically opposite angle)

∴∠COF = 115°

━━━━━━━━━━━━━━━━━━━━

ALL ANGLES :-

⋆ ∠AOE = 30°

⋆ ∠EOD = 115°

⋆ ∠BOD = 35°

⋆ ∠COF = 115°

$\color{purple}{HOPE}$ $\color{purple}{THIS}$ $\color{purple}{WILL}$ $\color{purple}{HELPS}$ $\color{purple}{YOU}$

Answer 2

From the figure,

↪∠ BOF = ∠ AOE

⇥∠ BOF = 40°

⇥∠ AOC = ∠ BOD

↪∠ AOC = 35°

[vertically opposite ∠ s]

[Given ∠ AOE = 40°]

[Vertically opposite ∠ s]

[given ∠ BOD = 35°]

Clearly, ∠ AOC + ∠ COF + ∠ BOF = 180°

↛35° + ∠ COF + 40° = 180°

↠∠ COF + 75° = 180°

↠∠ COF = 180°-75°

↠∠ COF = 105°.

$bts ❤ exo$