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Angles of a triangle are in A.P. and the greatest angle is double the least. Find the angles in circular measures.
A) 40, 60, 80
B) 40, 60, 50
C) 40, 70, 80
D) 20, 60, 80

Answer
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Hint:
Here we have to calculate the angles of a triangle. For that, we will first assume the three angles which will form an A.P with the same common difference. Then we will find the sum of all three angles and we will equate the sum with 180 as the sum of all the angles of a triangle is 180o. We will equate the greatest angle with twice the smallest angle. By solving these two equations, we will get the value of all the angles.

Complete step by step solution:
Let all the angles of a triangle which are in A.P be ad,a,a+d
We know the sum of all the angles of a triangle is 180o.
Now, we will find the sum of all the angles that we have assumed.
Sum of angles =ad+a+a+d=3a
We will equate the sum with 180o.
3a=180
Now, we will divide 180o by 3.
a=1803=60
Putting value in all the angles. The angles become 60d,60,60+d
We will now equate the greatest angle with twice the smallest angle.
Here the greatest angle is twice the smallest angle.
Therefore,
60+d=2(60d)
Now, we will use the distributive law of multiplication here.
60+d=1202d
Taking similar terms to the same sides, we get.
3d=60
Now, we will divide 60 by 3.
d=603=20
Putting value of d in all the angles, we get
60d=6020=4060+d=60+20=80

Therefore, the angles are
40,60&80
Thus, the correct option is A.


Note:
We have used distributive law of multiplication here for finding the product of 2 and 60d
Let there are four terms a,b&c then according to distributive law of multiplication a(b+c)=a.b+a.c
Here we have assumed angles asad,a,a+d. We can also take the angles a,a+d&a+2d instead of ad,a,a+d. As both of them are forming an A.P but we generally prefer ad,a,a+das it makes the solution easy and short.
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