Question

ABCD is an isosceles trapezium in which AB and CD are parallel.Find the other angles
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Answer 1

Answer:

So all angles are :

<A = 60°

<B = 120°

<C = 60°

<D = 120°

Step-by-step explanation:

Given,

ABCD is an isosceles trapezium.

And, <B = 120°

Then,

We know that sum of adjacent angles = 180°

Then,

<A + <B = 180°

=> <A + 120° = 180°

=> <A = 180° - 120° = 60°

Hence, <A = 60°

Now, if we extend AB from point A to its left side to E, we get,

<EAD + <DAB = 180° (linear pair)

=> <EAD + 60° = 180°

=> <EAD = 180° - 60° = 120°

Since, it is given AB II CD. Then, AD is transversal.

So,

<EAD = <ADC = 120° (Alternative Interior Angles)

Hence, <D = 120°

Now,

Since, trapezium is a quadrilateral. Then sum of all angles of quadrilateral = 360°

Then,

<A + < B + <C + <D = 360°

=> 60° + 120° + <C + 120° = 360°

=> 300° + <C = 360°

=> <C = 360° - 300° = 60°

Hence, <C = 60°

So all angles are :

<A = 60°

<B = 120°

<C = 60°

<D = 120°