
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
499.5k+ views
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 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
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
We will equate the sum with 180o.
Now, we will divide 180o by 3.
Putting value in all the angles. The angles become
We will now equate the greatest angle with twice the smallest angle.
Here the greatest angle is twice the smallest angle.
Therefore,
Now, we will use the distributive law of multiplication here.
Taking similar terms to the same sides, we get.
Now, we will divide 60 by 3.
Putting value of d in all the angles, we get
Therefore, the angles are
Thus, the correct option is A.
Note:
We have used distributive law of multiplication here for finding the product of 2 and
Let there are four terms then according to distributive law of multiplication
Here we have assumed angles as . We can also take the angles instead of . As both of them are forming an A.P but we generally prefer as it makes the solution easy and short.
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
Complete step by step solution:
Let all the angles of a triangle which are in A.P be
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
We will equate the sum with 180o.
Now, we will divide 180o by 3.
Putting value in all the angles. The angles become
We will now equate the greatest angle with twice the smallest angle.
Here the greatest angle is twice the smallest angle.
Therefore,
Now, we will use the distributive law of multiplication here.
Taking similar terms to the same sides, we get.
Now, we will divide 60 by 3.
Putting value of d in all the angles, we get
Therefore, the angles are
Thus, the correct option is A.
Note:
We have used distributive law of multiplication here for finding the product of 2 and
Let there are four terms
Here we have assumed angles as
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