ratio problem

[notgoodinmath]

If the ratio of the smallest to largest angle of a triangle is 2:7 and the ratio of the smallest to the next smallest angle is 1:3. What is the largest angle?


thanks

[yezz]

If the ratio of the smallest to largest angle of a triangle is 2:7 and the ratio of the smallest to the next smallest angle is 1:3. What is the largest angle?

smallest = 2x, largest = 7x

smallest to middle is 1:3 , ie 2x,6x

total angles = 180 = 6x+2x+7x = 15x, ie x = 12

7*12 = 84 degrees

[piyushdabomb]

I don't know if I was going about this the wrong way but couldn't I just use 3 equations and 3 unknowns?

1) x + y + z = 180
2) x + y + 7x = 180
3) x + 3x + z = 180

...and solve?

[deepamohn]

Smallest angle = S
largest angle = L1
2nd Largest angle = L2

Ratio of S/L1= 2/7
S/L2= 1/3

L1:S:L2 = 7: 2:6

Ans -> 7/15 (180) = 84