Question

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

Answer 1

hey friend here is your answer



let the three angle are (a),(a+d),(a-d) where smallest angle is (a-d) and greatest angle is (a+d)
sum of angle in. triangle =180°
a+a+d+a-d=180
3a=180
a=60
a+d=2(a-d)
a+d=2a-2d
d+2d=2a-a
3d=a
d=a/3. =60/3 =20
hence angle are (60),(60+20),(60-20)
=(60°),(80°),(40°)

hope it's helps

Answer 2

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Assumption

First term be p and common difference be d

Required angles are

p - d , p , p + d

As we know that :-

Sum of all angles of a triangle = 180°

Hence,

(p - d) + p + (p + d) = 180°

p - d + p + p + d = 180°

3p = 180°

p = 60°

Given,

Greatest angle is twice the least.

Greatest angle = 2 × Least angle

p + d = 2(p - d)

p + d = 2p - 2d

d + 2d = 2p - p

3d = p

Putting value of p from above

3d = 60°

d = 20°

Therefore, angles are :

p - d = 60° - 20° = 40°

p = 60°

p + d = 60° + 20° = 80°