in ABC, if A is thirteen less than C and B is eleven less than four times C, find the measure of each angle

Question

in ABC, if A is thirteen less than C and B is eleven less than four times C, find the measure of each angle

Answer 1

When you add up the 3 angles of a triangle, the sum is 180 degrees. So A + B + C = 180.

They say A is thirteen less than see, which means A = C - 13.

And we also know B is eleven less than 4 times C, which means B = 4C - 11.

To solve an equation we need to have only one unknown variable. If you have 2 unknown variables, technically it makes it impossible to solve the equation. For example in that first equation that we have for the sum of the triangles, we have 3 unknown variables (GEEZ!) but if we can find a way to have only one variable, we can solve the equation. Fortunately, if we replace A in terms of C, and then if we replace B in terms of C and we put them in the first equation we would only have the first equation in terms of C. So let's do it.

Since we have A + B + C = 180

Let's replace A in terms of C (since we know A = C - 13)

(C - 13) + B + C = 180

Now let's also replace B in terms of C

(C - 13) + (4C - 11) + C = 180

Now we have only one unknown variable in the equation, we can solve it.

C - 13 + 4C - 11 + C = 180

6C -24 = 180

6C =180 +24

6C = 204

Dividing both sides by 6, we then have C = 34.

And now it's easier to find B and C, we'll just plug C in the other equations.

We know A = C - 13, so A = 34 - 13

which gives us A = 21

And also we know B = 4C - 11, so B = 4x34 - 11

which gives us B = 125.

And we're done, so A = 21, B = 125 and C = 34.

For the sake of the explanation, the solution appears to be long but it's easier and shorter than it looks. If you have any question, let me know.