Choose the option which represents the maximum number of acute angles which a convex polygon can have.

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answer is B.

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Detailed Solution

We need to find the maximum number of acute angles which a convex polygon can have.
A convex polygon is a polygon with all the interior angle measures are less than

180 °

.
Next, an acute angle is the one which measures between

0 °

and

90 °

. Now, we have to state the maximum number of acute angles that a convex polygon can have.
Now, let us consider a convex quadrilateral, i.e., a polygon with four sides.
So, it will have four interior angles.
Now, let us assume that all the four interior angles of this convex quadrilateral are acute.
Now, we know that with every interior angle, there is an exterior angle.
So, if the interior angle is acute, then the exterior angle must be greater than

90 °

.
So, in case of our convex polygon, the sum of all the exterior angles will be greater than

360 °

, as all of them are greater than

90 °

.
But this is contradictory to the fact that for any quadrilateral, the sum of its exterior angles must be exactly equal to

360 °

.
So, we conclude that the convex quadrilateral that we considered with four acute interior angles is not possible, and can have a maximum of 3 acute angles.
Thus, in general, for a convex polygon, the maximum number of possible acute angles is 3.
Hence, the correct option is (2).

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