Question

Prove that a triangle must have at least two acute angles

Answer 1

sum of angles of triangle = 180*
Lets assume that only one angle have to be acute ei. <90*
Then the other two angle will have to be right or obtuse (90* and 90>) 
lets assume that both are of 90* (lowest possibility)
the the 3rd angle (x) which is an acute angle will be - 
180*= 90*+90*=X
 X = 180*- 90*-90* 
X= 0 
we know that an angle of a triangle cannot be 0
hence our assumtion is proved wrong! 
with this.. we can prove that a triangle MUST have atleast two angles acute..

Answer 2

Heya,

A triangle should have two acute angles and an obtuse angle or right angle to form a triangle.
Eg. 45°+45°+90°=180°
30°+30°+120°= 180°

A triangle cannot have two right angles because both the angles will together form 180° and they will not form a triangle.

Even, it cannot consist of two obtuse angles.

#hope this helps...

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