Can all the four angles of a quadrilateral be obtuse angles? Give reason for your answer.

Solution:

We know that

An obtuse angle is greater than 90º

From the angle sum property, the sum of all four angles of a quadrilateral is 360º

If we consider all the four angles more than 90º, the sum will be more than 360º

So all the four angles cannot be obtuse in a quadrilateral.

Therefore, all the four angles cannot be obtuse.

✦ Try This: Can the angles 100º, 50º, 50º and 160º be the angles of a quadrilateral? Why or why not?

The angles given are 100º, 50º, 50º and 160º

We know that the sum of all the angles of a quadrilateral is 360º

So the sum of the given angles is

100º + 50º + 50º + 160º = 360º

Therefore, 100º, 50º, 50º and 160º are the angles of a quadrilateral.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 8

NCERT Exemplar Class 9 Maths Exercise 8.2 Problem 7

Can all the four angles of a quadrilateral be obtuse angles? Give reason for your answer.

Summary:

A quadrilateral is a polygon with four sides, four angles and four vertices. No, all the four angles of a quadrilateral cannot be obtuse angles

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