Question

1. Prove that a triangle must have at least two acute angles.​

Answer 1

Answer:

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Solution:-

Sum of the three angles of a triangle = 180°

Let us assume that only one angle have to be acute i.e. less than 90°

Then the other two angles will have to be right or obtuse angles (90° or more than 90°)

Let us assume that both the angles are right angles (which is not possible)

Let the third angle be 'x', which is an acute angle.

⇒ 180° = x + 90° + 90°

⇒ x = 180° - 180°

x = 0

We know that an angle of a triangle cannot be 0.

Hence our assumption is completely wrong that two angles of a triangle are right angles. It cannot be possible.

Now, we can say that a triangle must have at least two acute angles.

Hence proved.

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Answer 2

Answer:

sum of all the angles of triangle is 180 degree

Step-by-step explanation:

let 1st angle be 60 degree

2nd angle be 20 degree

3rd angle will be 110 degreehere,

sum of all angles is 180 degree

now imagine,

1st angle is 60

2nd angle is 90

3rd angle is 110

sum of all the angles is not equal to 180

hence,

it is proved that in triangle 2 acute angles should be there