Question

(ii) The angles of a triangle are in AP. The greatest angle is twice the least .Find all the angles of the triangle.
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Answer 1

Answer:

All the angles of the triangle are (40, 60 and 80)degrees.

Step-by-step explanation:

Let the angles be a-d, a and a+d.

Given, a+d = 2(a-d)

=> a-2a = -2d-d

=> -a = -3d

=> a = 3d .....(i)

wWe know that the sum of all the angles of a triangle is 180 dgree, so,

a-d+a+a+d = 180 degree.

=> 3a = 180

=> a = 60 degree.

Now putting the value of a in equation (i), we obtain,

d = 30 degree.

Therefore, a-d, a, a+d = 40, 60 and 80 degrees respectively.

Hope it helps you...

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Answer 2

GIVEN :-

• The angles of a triangle are in AP .

• The greatest angle is twice the least angle .

TO FIND :-

• All the angles of the triangle .

SOLUTION :-

   

   Let the angles of the triangle be a - d , a and a + d .

   

   According to the question ,

   $\longrightarrow \sf a+d=2(a-d) \\\\\longrightarrow a+d =2a-2d \\\\\longrightarrow a-2a = -2d-d \\\\\longrightarrow -a = -3d\\\\\longrightarrow a = 3d \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ............(1)$

 Sum of all angles in a triangle = 180

   $\longrightarrow\sf a-d+a+a+d = 180\\\\\longrightarrow 3a = 180 \\\\\longrightarrow\bf a = 60$

Substitute a = 60 in equation (1) ,

   $\longrightarrow\sf 60=3d\\\\\longrightarrow \bf d = 20$

The angles of triangles are 40° , 60° and 80°.