Question

Find the value of



DEC in the given figure.​

Answer 1

Answer:

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In ∆ ABC :-

∠ CAB = ∠BAF - ∠CAF ⠀⠀⠀⠀ [straight angle pro. ]

⠀⠀⠀⠀ = 180° - 110°

⠀⠀ ⠀⠀ = 70°

& .. ∠ABC = 50° ⠀⠀⠀⠀ [ given ]

.•. ∠ACB = 180° - ( ∠CAB + ∠ABC ) ⠀⠀⠀⠀ [ angles sum pro. ]

⠀⠀⠀⠀ = 180° - ( 70° - 50° )

⠀⠀⠀⠀ = 180°- 120°

⠀⠀⠀⠀ = 60°

Now, In ∆ CDE :-

∠CDE = 22° ⠀⠀⠀⠀ [ given ]

& .. ∠ECD = 180° - ∠ACB ⠀⠀ ⠀⠀ [straight angle pro. ]

⠀⠀⠀⠀ = 180° - 60°

⠀⠀⠀⠀ = 120°

So, ∠DEC = 180° - ( ∠CDE + ∠ECD ) ⠀⠀⠀⠀ [ angles sum pro. ]

⠀⠀⠀⠀ = 180° - ( 22° + 120° )

⠀⠀⠀⠀ = 180° - 142°

⠀⠀⠀⠀ = 38°

${ { \tt{ { \color{blue}{ the \: required \: angle \: is \: {38}^{0} }}}}}$

${ { \tt{ \bold{ \color{red}{ \star \: hope \: it \: helps \: you\star}}}}}$

${ { \tt{ \bold{ \color{red}{ \star \: thanks\star}}}}}$

Answer 2

Answer:

ђєгє'ร ץ๏ยг คภรฬєг

∠ CAB = ∠BAF - ∠CAF ⠀⠀⠀⠀ [straight angle pro. ]

⠀⠀⠀⠀ = 180° - 110°

⠀⠀ ⠀⠀ = 70°

& .. ∠ABC = 50° ⠀⠀⠀⠀ [ given ]

.•. ∠ACB = 180° - ( ∠CAB + ∠ABC ) ⠀⠀⠀⠀ [ angles sum pro. ]

⠀⠀⠀⠀ = 180° - ( 70° - 50° )

⠀⠀⠀⠀ = 180°- 120°

⠀⠀⠀⠀ = 60°

Now, In ∆ CDE :-

∠CDE = 22° ⠀⠀⠀⠀ [ given ]

& .. ∠ECD = 180° - ∠ACB ⠀⠀ ⠀⠀ [straight angle pro. ]

⠀⠀⠀⠀ = 180° - 60°

⠀⠀⠀⠀ = 120°

So, ∠DEC = 180° - ( ∠CDE + ∠ECD ) ⠀⠀⠀⠀ [ angles sum pro. ]

⠀⠀⠀⠀ = 180° - ( 22° + 120° )

⠀⠀⠀⠀ = 180° - 142°

⠀⠀⠀⠀ = 38°

ђєภςє, Շђє гєợยเгє๔ คภﻮɭє เร 38° .

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