The smallest angle of a triangle is equal to 1/3 of the largest angle of a quadrilateral. The angles of the quadrilateral are in the ratio 4 : 5 : 6 : 9. The largest angle of the triangle is 4/3 times its smallest angle. Find the difference between the second-largest angle of the triangle and the second-smallest angle of the quadrilateral.

ATQ, Angles of the quadrilateral are in the ratio 4 : 5 : 6 : 9. Sum of angles of a quadrilateral = 360°. Total ratio parts = 4 + 5 + 6 + 9 = 24. One part = 360/24 = 15°. Smallest angle of quadrilateral = 4 × 15 = 60°. Second-smallest angle of quadrilateral = 5 × 15 = 75°. Largest angle of quadrilateral = 9 × 15 = 135°. Smallest angle of triangle = 1/3 of 135°. Smallest angle of triangle = 135/3 = 45°. Largest angle of triangle = 4/3 × 45 = 60°. Sum of angles of triangle = 180°. Third angle of triangle = 180 − 60 − 45 = 75°. Angles of triangle are 45°, 60° and 75°. Second-largest angle of triangle = 60°. Required difference = 75° − 60° = 15°.