I don't get this maths question?

Question

Okay, so I'm doing this maths homework. It's angles -

There's a triangle with TWO lines coming off it. On one of the lines there is a J. On the other side it says 84 degrees.

Inside the triangle it has K, M and 47. I have to work out what the letters are. Can anyone help me figure out how, please???

Answer 1

I take it that the letters are supposed to represent lengths of specific lines. Are these lines extensions of two different sides? ... of the SAME side, but in different directions? You didn't say. (Actually, I can't really see that it matters that there are two such lines; is that a red herring?) You also said: "On one of the lines there is a J." That's why it seems that J must represent a side; otherwise you would have said "One of the (exterior?) angles is called J." (You can't label an angle by a symbol "On a line" --- if it defines an angle, the symbol should be placed symetrically and clearly clearly within the relevant angle.)

There's similar ambiguity with writing "Inside the triangle it has K, M and 47." It matters where these are placed --- by the lines or at the angles.

Unfortunately, I find it impossible to visualize what you are describing; I doubt that others will be able to do so, either.

Could you try to be more specific in your description?

Thank you.

Answer 2

I assume that you are trying to determine the angles inside the triangle.

The lines coming off it are straight lines forming a 180 degree angle, so the angle J adjacent to the 84 degree angle is 96 degrees.

The other angle of the triangle would be 37 degrees because the three angles in the inside of a triangle always add up to 180 degrees. (37+47+96=180)

If the 84 degree angle is the opposite angle than the angles would be 47+49+96=180

Sorry but this is the best I can do with the information given.

Answer 3

You need to start with a known fact about all triangles, that the sum of the 3 angles always equals 180º. You also need to know that the sum of angles on a straight line equals 180º. Finally, we need to use the law of verticle angles are equivalent.

I'm going to guess where those letters and values are. If I'm off, just do the math with the general strategy described below. I'm also assuming that the "two lines" coming off the triangle are EXTENSIONS of the existing sides of the triangle.

So, for the straight line that is made up by angle J and 84º, we can use the following equation:

J + 84º = 180º
J = 96º

Now I've assumed that J is directly opposite K. That is, on the "X" made up by the triangle and two lines coming off it, the J and K are exactly opposite of each other. If this is true, then

J = K = 96º

Finally, the triangle angles must equal 180º, therefore

K + M + 47º = 180º
96º + M + 47º = 180º
M = 37º

Answer 4

the lines coming off the triangle are going to represent the supplemental angles to the angle adjacent to it ... ( the angle must be supplemental to 84, therefore the angle there = 96 degrees)

I'd need a diagram to figure the rest, but look at the picture....
the exterior 84 degree angle .... is equal to the sum of the non-adjacent angles.

so inside... K + M + 47 = 180, K = (133 - M), M =(133 - K)
then use the other exterior angle to be the sum of 47 plus the other letter