Question

AB||CD AND ANGLE F =30 DEGREES. FIND ANGLE FCD

Answer 1

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Answer 2

Step-by-step explanation:

$\bf \underline{Question-}$

In the given figure, AB||CD and angle F = 30°. Find angle FCD ?

$\bf \underline{Solution-}$

In ∆AFE,

∠AEF = 180° - (∠A + ∠F)

= 180° - (90° + 30°)

= 180° - 120°

= 60°

Now, ∠AEF = ∠BEC [Vert. opp. ∠s]

∴ ∠BEC = 60° [∵ ∠AEF = 60°]

Now, ∠BEC + ∠ECD = 180°

[∵ Sum of the interior ∠s on the same side of the transversal is 180°]

∴ ∠ECD = 180° - ∠BEC

∴ = 180° - 60° = 120°

Hence, ∠FCD = 120