In Fig., AB || CD and AE || CF; ∠FCG = 90° and ∠BAC = 120°. Find the values of x, y and z.

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Solution

$∠$ BAC = $∠$ ACG = 120° (Alternate interior angle)
∴ $∠$ ACF + $∠$ FCG = 120°
⇒ $∠$ ACF = 120° − 90° = 30°

$∠$ DCA + $∠$ ACG = 180° (Linear pair)
⇒ $∠$ x = 180° − 120° = 60°

$∠$ BAC + $∠$ BAE + $∠$ EAC = 360°
$∠$ CAE = 360° − 120° − (60° + 30°) = 150° ( $∠$ BAE = $∠$ DCF)

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In Fig., AB || CD and AE || CF; ∠FCG = 90° and ∠BAC = 120°. Find the values of x, y and z.

∠BAC = ∠ACG = 120° (Alternate interior angle) ∴ ∠ACF + ∠FCG = 120° ⇒ ∠ACF = 120° − 90° = 30° ∠DCA + ∠ACG = 180° (Linear pair) ⇒∠x = 180° − 120° = 60° ∠BAC + ∠BAE + ∠EAC = 360° ∠CAE = 360° − 120° − (60° + 30°) = 150° (∠BAE = ∠DCF)