Question

find x in the following figure​

Answer 1

$\huge\sf\pink{Answer}$

☞ The Value of x is 120°

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$\huge\sf\blue{Given}$

✭ ∠BAE = 105°

✭ ∠AEC = 15°

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$\huge\sf\gray{To \:Find}$

◈ Value of ∠ECD (x)?

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$\huge\sf\purple{Steps}$

$\underline{\underline{\sf Construction}}$

◕ Extend CD to F & AB ll FD and AE is the transversal

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$\underline{\underline{\sf Concept}}$

➝ Corresponding Angles are equal

➝ Angles of a triangle add up to 180°

➝ Linear Pair means it forms a straight angle i.e 180°

So on solving we see that,

➳ ∠BAE = ∠EFD

➳ ∠EFD = 105°

In ∆EFC,

➠ ∠FEC + ∠EFD + ∠ECF = 180° «« Angle Sum Property »»

➠ 15° + 105° + ∠ECF = 180°

➠ 120° + ∠ECF = 180°

➠ ∠ECF = 180° - 120°

➠ ∠ECF = 60°

So now,

»» ∠ECF + ∠ECD = 180° «« Linear Pair »»

»» 60° + ∠ECD = 180°

»» ∠ECD = 180° - 60°

»» ∠ECD = 120°

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