# What is the maximum number of obtuse angles that a quadrilateral can have ?

(a) 1

(b) 2

(c) 3

(d) 4

**Solution:**

We have to find the maximum number of obtuse angles that a quadrilateral can have.

An obtuse angle is defined as an angle that is greater than 90° and less than 180°.

We know that the sum of all the four interior angles of a quadrilateral is 360 degrees.

case(i) : If all the angles are obtuse

Let four angles be a, b, c and d

Let a = 100°, b = 120°, c = 110° and d = 150°

Sum of all angles = a + b + c + d

= 100°+ 120° + 110° + 150°

= 480° > 360°

All angles cannot be obtuse.

case(ii) : If three angles are obtuse

Let a = 100°, b = 110° and c = 120°

100° + 110° + 120° + d = 360°

330° + d = 360°

d = 360° - 330°

d = 30°

Therefore, the maximum number of obtuse angles can be 3.

**✦ Try This: **What is the maximum number of acute angles that a quadrilateral can have ?

**☛ Also Check: ** NCERT Solutions for Class 8 Maths

**NCERT Exemplar Class 8 Maths Chapter 5 Problem 12**

## What is the maximum number of obtuse angles that a quadrilateral can have ? (a) 1 (b) 2 (c) 3 (d) 4

**Summary:**

The maximum number of obtuse angles that a quadrilateral can have is 3.

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