State true or false:

Triangle is a polygon whose sum of exterior angles is double the sum of interior angles.

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True

False

answer is A.

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Detailed Solution

Given a statement, triangle is a polygon whose sum of exterior angles is double the sum of interior angles.
We need to find whether the given statement is true or false.
The angle sum property of a polygon says that the sum of all the interior angles of a triangle is always

180 ∘

.
Now, we know that with every interior angle, there exists an exterior angle which is formed by a side of a triangle and an extension of the adjacent side.
So, let us consider a triangle with its interior and exterior angles as follows,
Question Image

Now, applying the angle sum property in the above triangle, we get,

∠ x + ∠ y + ∠ z = 180 ° ......... (i)

Now, we know that a pair of an exterior and interior angle at a location is always supplementary.
Using this fact, we can express the exterior angles of the triangle in terms of its interior angles as follows,