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

Posted by Suhas Chinnu 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Let the three angles of triangle which are in A.P. be a - d, a, a + d
Now, sum of the angles = 180°
{tex}\Rightarrow{/tex} a - d + a+ a + d = 180°
{tex}\Rightarrow{/tex} 3a = 180°
{tex}\Rightarrow{/tex} a = 60°
It is given that,
a + d= 2(a - d)
{tex}\Rightarrow{/tex} a + d = 2a - 2d
{tex}\Rightarrow{/tex} a = 3d
{tex}\Rightarrow{/tex} 60° = 3d
{tex}\Rightarrow{/tex} d = 20°
Thus, the angles of triangle are 40°, 60°, 80°.

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