Question

Show that at least two angles in a triangle are acute

Answer 1

If one angle is 90 or more

Sum of all three angles of a triangle is 180

So, other two angles will be equal to or less than 180-90, so they will be acute angles.

Answer 2

Sum of angle of triangle = 180°

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

Then other to angle will have to be

Right or Obtuse angle.(90° or > 90°)

Let assume that both are 90°;then the third angle (X) which is an acute angle will be,

180° = 90 + 90 + X

X = 180 - 90 - 90

X = 180 - 180

X = 0°

We know that an angle of triangle can not be 0°

Therefore, our assumption was wrong. So, triangle have atleast two acute angle.

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