The interior angles of a triangle are 2a-3b, 4a-b, 6a+4b, where a and b are positive integers. If the measure of the smallest angles is 24 degree, then what is the measure of the greatest angle?

a) 62 degree

b) 86 degree

c) 74 degree

d) 98 degree

The interior angles of the given triangle are given as 2a − 3b, 4a − b, and 6a + 4b.

It is known that the sum of all the interior angles of a triangle is 180°.

∴2a − 3b + 4a − b + 6a + 4b = 180°

⇒ 12a = 180°

∴2a − 3b = 2 × 15° − 3b = 30° − 3b

4a − b = 4 × 15° − b = 60° − b

6a + 4b = 6 × 15° + 4b = 90° + 4b

Therefore, the interior angles of the given triangle are 30° − 3b, 60° − b, and 90° + 4b.

It is clear that the smallest angle is 30° − 3b, whereas the greatest angle is 90° + 4b

It is given that the measure of the smallest angle is 24°.

Thus, the greatest angle is 90° + 4b = 90° + 4 × 2° = 98°.

The correct answer is D.