Question

The measure of angles of triangle are in A.P. The smallest angle is 40. Find the angles of the triangle in degree and in radian

Answer 1

In degree

= 40°, 60°, 80°

In radian

= 0.698, 1.047, 1.396

Answer 2

Given

The smallest angle of a triangle is 40°

The measure of angles of a triangle is in arithmetic progression

To Find

The angles of the triangle in degrees and in radians

Solution

We know that the sum of all angles of a triangle is 180°

Since the angles of the triangle follow an Arithmetic progression, lets us assume the difference between the angles as 'd'.

Now the smallest angle is given as 40°

Hence sum of all angles of the triangle = 40+40+d+40+2d = 180

120+3d = 180

3d = 60

d = 20

Hence the angles of the triangle in degrees are 40, 60, 80 and in Radians are 0.698132, 1.0472, 1.39626