Question

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

Answer 1

$\Huge\mathcal{\underline{\blue{Answer\::-}}}$

Required angles are 40° , 60° and 80° .

$\Large{\pink{Explanation\::}}$

Let, required angles are a - d , a and a + d, since they are in arithmetic progression.

From the properties of triangles :

sum of all angles of a triangle is 180°.

Thus,

➟ ( a - d ) + a + ( a + d ) = 180°

➟ a - d + a + a + d = 180°

➟ 3a = 180°

$\purple{➟\:a = 60°}$

Given, Greatest angle is twice the least.

$\orange{➟\:Greatest\:angle = 2\:x\:least\: angle}$

➟ a + d = 2( a - d )

➟ a + d = 2a - 2d

➟ d + 2d = 2a - a

➟ 3d = a

➟ 3d = 60° { from above, a = 60° }

$\green{➟\:d = 20°}$

Therefore, angles are :

• a - d = 60° - 20° = 40°
• a = 60°
• a + d = 60° + 20° = 80°

Hence the required angles are 40° , 60° and 80° .

$\Huge\mathcal{\underline{\red{Hope\:It\: Helps}}}$