Question

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Answer 1

Step-by-step explanation:

Question: In the given figure,AB||CD and AE||CF; ∠FCG = 90° and ∠BAC = 120° . Find the value of x, y and z.

To find: The value of x, y and z.

Sol. AB || CD and AE || CF and ∠FCG = 90° and ∠120°

• Line AB || line CD

∴ ∠BAC and ∠ACD are supplementary angle.

Sum of supplementary angle is 180°

∴ ∠BAC + ∠ACD = 180°

=> 120° + x = 180°

=> x = 180° - 120°

=> x = 60°

Also,

∠CDA + ∠ACF + ∠FCG = 180°

=> x + y + 90° = 180°

=> 60° + y + 90° = 180°

=> y + 150° = 180°

=> y = 180° - 150°

=> y = 30°

Line AE || line CF

∴ ∠EAC and ∠ACF are supplementary angle.

Sum of supplementary angle is 180°

∴ ∠EAC + ∠ACF = 180°

=> z + y = 180°

=> z + 30° = 180°

=> z = 180° - 30°

=> z = 150°

Answer:-

Hence, the value of x is 60°, y is 30° and z is 150°.