Can all the angles of a quadrilateral be acute angles? Give reason for your answer.
Solution:
We know that
From the angle sum property of a quadrilateral the sum of all angles is 360º
If all the angles are acute, then the sum will not be 360º
Therefore, all the angles of a quadrilateral cannot be acute.
✦ Try This: In ∆ABC, AB = 5 cm, BC = 10 cm and CA = 15 cm. If D and E are respectively the mid-points of AB and BC, determine the length of DE.
It is given that, in ∆ABC
AB = 5 cm
BC = 10 cm
CA = 15 cm
D and E are respectively the mid-points of AB and BC
We have to find the length of DE
Using the mid-point theorem
DE = 1/2 AC
Substituting the values
DE = 1/2 (15)
DE = 7.5 cm
Therefore, the length of DE is 7.5 cm.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 8
NCERT Exemplar Class 9 Maths Exercise 8.2 Problem 11
Can all the angles of a quadrilateral be acute angles? Give reason for your answer.
Summary:
No, all the angles of a quadrilateral cannot be acute angles as the sum of all the angles will not be equal to 360º
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