Question

the angles of a triangles are in A.P such that greatest is 5 times the least. Find the angles in radians

Answer 1

Since the angles are in A.P

Let the angles be x-d, x,  x+ d. (Where d= common difference)

ATQ, Greatest is 5 times the least, which means- 

⇒x+ d = 5( x- d)
⇒x+ d= 5x - 5d
⇒ 4x = 6d
⇒ d= 4x/ 6

Now, we know that the sum of these angles will be 180° (Angle Sum Property)

⇒ x-d + x + x+ d= 180
⇒ 3x = 180
⇒ x= 60

So d= (4* 60) /6 
= 240/6
= 40

Thus the angles will be 20°, 60°, 100°

Answer 2

Answer:

see answer ❤

Step-by-step explanation:

Since the angles are in A.P

Let the angles be x-d, x,  x+ d. (Where d= common difference)

ATQ, Greatest is 5 times the least, which means-  

⇒x+ d = 5( x- d)

⇒x+ d= 5x - 5d

⇒ 4x = 6d

⇒ d= 4x/ 6

Now, we know that the sum of these angles will be 180° (Angle Sum Property)

⇒ x-d + x + x+ d= 180

⇒ 3x = 180

⇒ x= 60

So d= (4* 60) /6  

= 240/6

= 40

Thus the angles will be 20°, 60°, 100°