The angles of a triangle are in AP. The greatest angle is twice the least. Find all the angles of the triangle
Solution:
Given ,
The angles of a triangle are in AP.
Consider A, B and C are angles of a ∆ABC
B = (A + C)/2
2B = A + C …(i)
We know that, the sum of all interior angles of a ∆ABC is 180°
A + B + C = 180°
2B + B = 180° [from Equation (i)]
3B = 180°
B = 60°
Let A and C be the greatest and least angles
A = 2C …………. (ii)
Substituting the values of B and A in Equation (i),
2 × 60° = 2C + C
120° = 3 C
C = 40°
Substitute value of C in Equation (ii),
A = 2 × 40°
A = 80°
Therefore, all the angles of a triangle are 80°, 60° and 40°.
✦ Try This: The angles of a triangle are in AP. The greatest angle is thrice the least. Find all the angles of the triangle
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5
NCERT Exemplar Class 10 Maths Exercise 5.3 Problem 13
The angles of a triangle are in AP. The greatest angle is twice the least. Find all the angles of the triangle
Summary:
The angles of a triangle are in AP. The greatest angle is twice the least. All the angles of a triangle are 80°, 60° and 40°
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