Question

The angels of a triangle are in AP . The greatest angel is twice the smallest angle find all angles of triangle?​

Answer 1

Answer:

Let A,B and C be the three angles in AP.( in degree)

And A being the least and C being the greatest

Than

so, C = 2A [ Given ] ( Equation 1)

B - A = C - B

2B = A + C

2B = A + 2A ( using Equation 1 )

2B = 3A

B = 3A/2 ( Equation 2 )

using the angle of the sum property of triangle

A + B + C = 180°

A + 3A/2 + 2A = 180° ( using Eqⁿ 1 and 2 )

2A + 3A + 4A whole divided by 2 = 180 °

so, 9A = 360

A = 360/9

A = 40°

so, B = 3(40)/2 ( using eqⁿ 2 )

B = 60°

and, C = 2(40) ( using eqⁿ 1 )

C = 80°