Question

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

Answer 1

Step-by-step explanation:

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°. Therefore, the interior angles of the given triangle are 30° − 3b, 60° − b, and 90° + 4b. It is given that the measure of the smallest angle is 24°.

Answer 2

Step-by-step explanation:

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°

a=180/12=15

∴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°.

therefore ,30 dergree - 3b = 24 degree

30 - 24 = 3b

3b = 6

b = 6/3

b = 2

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