In a triangle , the greatest angle is 20`more than twice the middle angle and the smallest angle is 40` iess than the middle angle. Find all the angles of the triangle. What type of triangle is it?

Solution:

Let us assume the smaller angle of the triangls be Ao.

from the problem we get : the middle angle is 40o more than the smaller angle the larger angle is 20o more than the twice the middle angle.

So middle angle = (Ao + 40o) and Larger angle = {2( Ao + 40o ) + 20}

As we know that the sum of three angle of a triangle = 180o.

Then A + (A + 40) + {2( Ao+ 40o) + 20} = 180

A + A + 40 + { 2A + 80 + 20} = 180

A + A + 2A = 180 - 40 - 80 - 20

4A = 40

A = 40/4 = 10o

Since the middle angle is 40omore than the smaller angle then the middle angle = ( 10 + 40) = 50o.

and the larger angle is 20omore than the twice the middle angle, then the larger angle = 2 x 50 + 20 = 120o.

As the all three angles are different then the Triangle is a Scalene triangle.

Ans: 10o, 50o, 120o Scalene Triangle.