find x in the following figure
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☞ The Value of x is 120°
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✭ ∠BAE = 105°
✭ ∠AEC = 15°
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◈ Value of ∠ECD (x)?
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◕ Extend CD to F & AB ll FD and AE is the transversal
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➝ 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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