Question

the angles of a triangle are in AP. the greatest angle is twice the least . find all the angles.​

Answer 1

Let a be the smallest angle in the A.P.

The largest angle = 2a.

Sum of the terms = 180 [Sum of the angles of a triangle].

$S_{n} = \frac{n}{2} (a + l) \\ \\ 180 = \frac{3}{2} (a + 2a) \\ \\ \frac{360}{3} = 3a \\ \\ a = \frac{360}{9} = 40 \\ \\ 2a = 2(40) = 80$

The 3rd angle = 180 - (40+80) = 180 - 120 = 60.

Therefore, the angles of the triangle are: 40°,60° and 80°.

Answer 2

Answer:-

$(a - d, a, a + d)$

The triangle that form AP there are three angles

Twice the greatest angle

$(2(a - d) = a + d 2a - 2d = a + d a = 3d)$

property used here (ASP) angle sum property

Angle sum property

$(a - d) + a + (a + d) = 180° 3a = 180° a = 60°)$

$(3d = 60° d = 20° )$

$(a - d = 60°- 20° = 40° a = 60° )$

$(a + d = 60° + 20° = 80°)$

answer=80 degree