The angles of a triangle are in AP (arithmetic progression). If measure of the smallest angle is $$50^\circ$$ less than that of the largest angle, then find the largest angle (in degrees).

The angles of triangle are in AP (arithmetic progression).

Let the angles are a, a+r, a+2r.

Measure of the smallest angle is $$50^\circ$$ less than that of the largest angle.

a = a + 2r - $$50^\circ$$

2r = $$50^\circ$$

r = $$25^\circ$$

Sum of the angles of triangle = $$180^\circ$$

a + a + r + a + 2r = $$180^\circ$$

3a + 3r = $$180^\circ$$

3a + $$75^\circ$$ = $$180^\circ$$

3a = $$105^\circ$$

a = $$35^\circ$$

Largest angle of triangle = a + 2r = $$35^\circ$$ + $$50^\circ$$ = $$85^\circ$$

Hence, the correct answer is Option B