
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
494.4k+ 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
Recently Updated Pages
Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Master Class 11 Social Science: Engaging Questions & Answers for Success

Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Trending doubts
How many moles and how many grams of NaCl are present class 11 chemistry CBSE

How do I get the molar mass of urea class 11 chemistry CBSE

Define least count of vernier callipers How do you class 11 physics CBSE

Plants which grow in shade are called A Sciophytes class 11 biology CBSE

A renewable exhaustible natural resource is A Petroleum class 11 biology CBSE

In which of the following gametophytes is not independent class 11 biology CBSE
