Question

The measures of the angles of a triangle are in the extended ratio 3:6:11. what is the measure of the largest angle?

Answer 1

??

Answer 2

The side that has length 11 is too long to work with sides of lengths 3 and 6 to be able to have a triangle.

Answer 3

Yes: in other words, if the sides of length 3 and 6 were to be lined up straight, their combined length would come to 9, whereas the length of the longest side would be 11. No soap.

Answer 4

well the question isnt wrong. idk=/ something like 20x +6x + 11x = 180 ??

Answer 5

Sorry. Ignore what I wrote above. I misread the question.

Answer 6

It's the angles that are in that ratio, not the sides. My mistake.

Answer 7

the answer is 99 .. i think. thats my guess.

Answer 8

Oh, shoot. RED face. We were talking about side lengths here; the problem deals with ANGLES, not side lengths.
If x is a constant of proportionality, then 3x+6x+11x=180 degrees (because the interior angles of a triangle always sum up to 180 degrees).

Answer 9

Since the angles are in the 3:6:11 ratio,
let's call the angles 3x : 6x : 11x

That means 3x + 6x + 11x = 180

Answer 10

Now we solve for x:

3x + 6x + 11x = 180
20x = 180
x = 9

Answer 11

Your guess? Just add up 3x and 6x and 11x and set them equal to 180; result is 20x=180. x+??

Answer 12

9 isnt an option

Answer 13

so 20?

Answer 14

Since we know x = 9, and the angle is 11x, we replace the x with 9:

11x = 11*9 = 99

Answer 15

yay i was right :D thanks!

Answer 16

Right. 9 is nothing more than a constant multiplier. 9 is not a measure of one of the angles. Mathstudent has the right idea.