Question

Its tooooooooooooo urgent.plz solve

Answer 1

An equilateral triangle is that whose each angle measures 60 degree. 

So, 2/3 of a right angle is same as 60 degree.

According to the law of sines,

The angle opposite to the longest side will be greater angle. 

In a triangle, 

as we know that , the sum of  three angles of a triangle = 180 degree.

where at least one of the angles must be equal to or at least should be 60 degree. 

Also, the greater angle can't be 60 degree. It must be more than 60 degree.

Answer 2

The question states that the angle must be greater than two-third of right angle i.e it must be greater than 60°

Suppose AC is the greatest side (shown in the image above)

then, AC > AB
angle B > angle C --------(i)

and
AC > BC
angle B > angle A ----------(ii)

add (i) and (ii)

2 (angle B) > angle C + angle A

now add angle B on both the sides.

3 (angle B) > angle C + angle A + angle B

as we know that sum of all angles in a triangle equals 180°

So,

3 (angle B) > 180°

angle B > 60°

Thus, proves that the angle opposite to longest side must measure greater than 60°.