State true or false:

A quadrilateral can have all four interior angles as obtuse.

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True

False

answer is B.

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Detailed Solution

Here, we have to state if all the interior angles of a quadrilateral can be obtuse or not.
So, by the definition of an obtuse angle, it is the angle measure which is greater than

90 °

but less than

180 °

.
Also, by the angle sum property of a quadrilateral, the sum of all the interior angles if a quadrilateral is exactly

360 °

.
Now, if all the four interior angles of a quadrilateral are obtuse, then a closed two-dimensional shape with four sides will never be possible.
Also, the sum of the interior will never be exactly equal to

360 °

, which means that the angle sum property won’t be satisfied as well.
So, any quadrilateral can never have all four interior angles as obtuse.
Hence, the given statement is false.
Hence, the correct option is (2).

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