Question

The 3 angles of a triangle are in AB and the biggest angle is given 105 degree. Find all the angles of a triangle.

Answer 1

Step-by-step explanation:

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°.