State true or false:

The sum of interior angles and the sum of exterior angles taken in an order are equal in case of quadrilaterals only.

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True

False

answer is A.

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Detailed Solution

Given a statement, the sum of interior angles and the sum of exterior angles taken in an order are equal in case of quadrilaterals only.
We need to check if the given statement is true or false.
The angle sum property of a quadrilateral states that the sum of all the interior angles of a quadrilateral is always

360 °

.
Now, as per the statement, the sum of all the exterior angles must also be

360 °

.
So, we have, a quadrilateral as follows,
Question Image

Now, as per the definition of an exterior angle of a quadrilateral, it is the angle formed by a side and an extension of the adjacent side.
Also, we know that an interior angle and an exterior angle together form a supplementary pair.
Thus, in the above quadrilateral, we have, the sum of all the exterior angles corresponding to each interior angle as follows,