Question

The internal angles of a triangle are in A.P. If the smallest angle is 45°, find the remaining angles.

Answer 1

Since the angles are in an Arithmetic Progression (A.P.), let the three angles be First (smallest) angle = a, Second angle = a + d, and Third angle = a + 2d (where d is the common difference).

The sum of all internal angles in a triangle is 180°.

a + (a + d) + (2 + 2d) = 180°

3a + 3d = 180°

We are given that the smallest angle is 45°.

3(45°) + 3d = 180°

135° + 3d = 180°

3d = 180° − 135°

3d = 45°

d = `45/3`

d = 15°

Second angle = a + d

= 45° + 15°

= 60°

Third angle = a + 2d

= 45° + 2(15°)

= 45° + 30°

= 75°

Hence, the angles are 45°, 60°, and 75°.