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:
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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