Question

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

Answer 1

Answer:

40,60 and 80

Step-by-step explanation:

Let the angles of triangle are a-d, a, a+d.

In a triangle, sum of all angles = 180

a-d +a+ a+d= 180

3a = 180

a = 60 .

Given - a+d = 2a-2d

a = 3d

we know, a =60

3d = 60

d = 20

so angles are 40, 60 and 80

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Answer 2

Solution:

As we know that in a AP

AP = a + d , a , a - d

Here ,

• Greatest angle = a - d
• Smallest angle = a + d

Now , finding all the angles in the ∆ using angle sum property

Sum of all the angles in the ∆ = 180°

→ a + (a + d) + (a - d) = 180°

→ a + a + d + a - d = 180°

→ 3a = 180°

→ a = 60°

From the above question greatest angle is twice the least . Let the least angle be x then the greatest angle will be 2x. Here , x will be the least = a + d

In the other form

→ 2(a - d) = a + d

→ 2a - 2d = a + d

→ 2a - 2d - (a + d) = 0

→ 2a - 2d - a - d = 0

→ a - 3d = 0

→ a = 3d

→ 3d = 60°

→ d = 20°

Now finding all the angles

★ a + d

♦ 60° + 20° = 80°

★ a

♦ 60°

★ a - d

♦ 60° - 20° = 40°

Hence , all angles = 80° , 60° & 40°