Question

the angles of a triangle are in ap. if its greatest angle is twice the least,find all the angles of the triangle
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Answer 1

Answer:

Step-by-step 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°

= > a = 60°

Given,

Greatest angle is twice the least.

= > 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° }

= > 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° .

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