Question

What is the maximum number of obtuse angles that a quadrilateral has?
A.1
B.2
C.3
D.4

Answer 1

Hint: We know that an obtuse angle is greater than \[{90^ \circ }\]. And since the sum of all interior angles is \[{360^ \circ }\], we need to check the maximum possibility of the angles that can be obtuse.

Complete step-by-step answer:
We know that quadrilateral means a polygon with four sides and four angles.
Now one of the angles can be an obtuse in the simplest case.
But we can have one, more angle to be obtuse then the remaining two angles should be definitely acute.
Because if two angles are obtuse (taking the lowest measure of an obtuse angle as \[{91^ \circ }\] ) then \[{360^ \circ } - {182^ \circ } = {178^ \circ }\]
Now this remaining measure cannot be taken as a full angle because the quadrilateral is having four angles. But it can be splitted into one obtuse and another acute angle.
Thus a quadrilateral can have the three angles as obtuse.
So the correct option is C.
So, the correct answer is “Option C”.

Note: Note that three obtuse angles are possible but we generally see only two obtuse angles in the quadrilateral we draw. The rectangle and square have all right angles but in case of parallelogram and rhombus we can see the two angles to be obtuse.