Question

The angle of a triangle are in A.P if the greatest angle is twice the least. Find the angles.

Answer 1

Let a - d, a, a + d be the three angles of the triangle that form AP.

Given that the greatest angle is twice the least.

Now, 2(a - d) = a + d

2a - 2d = a + d

a = 3d ---------------(1)

Now by angle sum property,

(a - d) + a + (a + d) = 180°

3a = 180°

a = 60°----------------------(2)

from (1) and (2),

3d = 60°

d = 20°

Now, the angles are,
a - d = 60°- 20° = 40°
a = 60°
a + d = 60° + 20° = 80°.

THE ANGLES ARE : 40°, 60° & 80 °

Hope the answer is clear !

Answer 2

Let the angles be = x, y, z  ( these are in AP)

Since it is a triangle, x+y+z= 180

Given, z=2x
therefore, x+y+z= x+y+2x = 3x+y=180.....................(1)

The new angles in AP are --> x, y, 2x 
  Using property of AP,   y-x = 2x-y
                                      2y = 3x
                                      y= 3x/2
Substituting the value of y in equation (1)
 3x+ 3x/2 = 180
6x + 3x = 360
9x = 360
x= 40 degree

z= 2x = 80 degree

y= 3x/2
y= 3*40/2
y= 60 degree

The angles of the triangle are 40 degree, 60 degree and 80 degree

Thankyou