wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Question 183
Find the maximum number of acute angles which a convex quadrilateral, a pentagon and a hexagon can have. Observe the pattern and generalise the result for any polygon.

Open in App
Solution

Let us assume that a convex polygon has four or more acute angles. If an interior angle is acute, then the corresponding exterior angle will be obtuse ( greater than 90). So, the sum of the exterior angles of such a polygon will be greater than 4×90=360.
However, this is impossible, since the sum of the exterior angles of a polygon must always be equal to 360. Hence, a polygon can have, at most, 3 obtuse exterior angles.

flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Introduction to Quadrilaterals
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon