Math, asked by shruti7455, 1 year ago

a quadrilateral have 4 acute angle or 3 obtuse angles please answer

Answers

Answered by Leukonov
19
The angles which are greater than 90° are called Obtuse and Those which are less than 90° are called acute angles...

Now...

Lets imagine a Quadrilateral with 3 of its angles as 100°

By Angle sum Propert of a Quadrilateral The third side is 360°-3(100°) =60°

Now let The angle of the three sides be 91°
The third side is 360°-(3(91°))=(360°-273°)=87°

Hence, A quadrilateral Can have 3 obtuse angles...

Now Lets imagine a Quadrilateral With 3 sides of its angle as 89°
So it Fourth side is [360°-3(89°)=360°-267°=]103°. which is an obtuse...

But 89° is the largest of the acute angles and if three angle with largest acute angle is present The foirth angle of a quadrilalateral determines if 4 acute angles can be formed for a quadrilateral...
But it is not Possible...

Hence only The First statement is correct!

Hope it Helps...
Regards,
Leukonov.
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