- We now in a triangle sum of any two sides is greater
than the thirdside. Is the sum of any two angles of a
triangle also greater than the third angle? Justify Or
contradict with an example
Answers
it is not necessary that sum of any two angle of a triangle is greater than the third angle
Step-by-step explanation:
we know in a triangle sum of any two sides is greater than the third side
But it is not necessary that sum of any two angle of a triangle is greater than the third angle
Example A right angle Triangle
where sum of two acute angles = Third angle (90°)
An obtuse angle triangle
where sum of two acute angles < obtuse angle
for example 30° + 30° < 120°
as a triangle has a + b + c = 180°
a + b = 180° - c
if a + b > c
=> 180° - c > c
=> 2c < 180°
=> c < 90°
Hence only acute angle triangle will satisfy sum of any two angle of a triangle is greater than the third angle
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