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Question
Is the following statement true and false :
If one angle of a triangle is obtuse, then it cannot be a right angled triangle.
Options
Ture
False
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Solution
If one angle of a triangle is obtuse, then it cannot be a right angles triangle.
According to the angle sum property of the triangle
In ΔABC
∠A +∠B + ∠C = 180°
Now, if it is a right angled triangle
Then,
∠A + ∠B + ∠C = 180°
90° + ∠B + ∠C =180°
∠B +∠C = 90°
Also if one of the angle’s is obtuse
∠B +∠C > 90°
This is not possible.
Thus, if one angle of a triangle is obtuse, then it cannot be a right angled triangle.
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