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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