# 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

**☛ Related Questions:**

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