Question

Three angles of a triangle are in AP. The greatest angle is twice the least. Find all the angles of the

triangle.​

Answer 1

Solution :

Let three angles of a triangle are in A.P. are;

• a
• a+d
• a+2d

A/q

$\longrightarrow\tt{a+2d=2a}\\\\\longrightarrow\tt{a-2a=-2d}\\\\\longrightarrow\tt{-a=-2d}\\\\\longrightarrow\tt{a=2d}$

Putting the value of a above given three angles,we get;

• 2d
• 2d+d = 3d
• 2d+2d = 4d

We know that sum of three angle of triangle = 180°

$\longrightarrow\tt{2d+3d+4d=180\degree}\\\\\longrightarrow\tt{9d=180\degree}\\\\\longrightarrow\tt{d=\cancel{\dfrac{180\degree}{9} }}\\\\\longrightarrow\tt{d=20\degree}}$

Thus;

• 1st angle of triangle = 2d = 2(20°) = 40°
• 2nd angle of triangle = 3d = 3(20°) = 60°
• 3rd angle of triangle = 5d = 4(20°) = 80°