Question

The opposite sides of a quadrilateral are parallel. If one angle of the quadrilateral is 60°,find the other angles.
Draw the diagram and explain in perfect plz

Answer 1

$Hey\:There$
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Refer to attachment for the diagram.

Given ,the opposite sides of a quadrilateral are parallel. So, it is a parallelogram.

And given one angle of quadrilateral is 60°.
As we know, opposite angles of a parallelogram are equal.
Thus the opposite angle is also 60°.

Now, see the diagram.

angle DAB = angle DCB i.e., 60°

angle DAB + angle DCB + angle CDA + angle ABC = 360°
[Sum of angles of a parallelogram is 360°]

=> 60° + 60° + angle CDA + angle CDA = 360°
[Opposite angles of a parallelogram are equal]

=> 120° + 2 angle CDA = 360°

=> 2 angle CDA = 360° – 120°

=> 2 angle CDA = 240°

=> angle CDA = 240° / 2

=> angle CDA = angle ABC = 120°

Hence, the other angles of quadrilateral are 60°, 120° and 120°.
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$Hope\:my\:ans.'s\:satisfactory.$(^-^)

Answer 2

Answer:

Given ,the opposite sides of a quadrilateral are parallel. So, it is a parallelogram.

And given one angle of quadrilateral is 60°.

As we know, opposite angles of a parallelogram are equal.

Thus the opposite angle is also 60°.

Now,

angle DAB = angle DCB i.e., 60°

angle DAB + angle DCB + angle CDA + angle ABC = 360°

[Sum of angles of a parallelogram is 360°]

=> 60° + 60° + angle CDA + angle CDA = 360°

[Opposite angles of a parallelogram are equal]

=> 120° + 2 angle CDA = 360°

=> 2 angle CDA = 360° – 120°

=> 2 angle CDA = 240°

=> angle CDA = 240° / 2

=> angle CDA = angle ABC = 120°

Hence, the other angles of quadrilateral are 60°, 120°

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