Question

prove that a triangle must have at least two acute angles.

Answer 1

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.

Answer 2

Answer:

Step-by-step explanation:

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