In ABC, m<B is 5 times m<A and m<C is 17 degrees less than 4\ times m<A. What equation is used to solve for the variable x?

Answer 1

Hi there, heres how you'd set up this problem. I hope this helps.

ABC is a triangle so the total degrees is equal to 180.

1. m < B = 5(< A)
2. m < C = 4(< A) - 17
3. m < A = x

So if we know each equation for each angle, we add each angle to equal a total of 180.

180 = A + B + C

180 = 5(x) + 4(x) - 17 + x

Distribute, then combine like terms.

180 = 5x + 4x -17 +x

180 = 10x - 17

Add 17 to both sides of the equation so your variables are only on one side.

180 = 10x - 17

+17 +17

---------------------

180 + 17 = 10x

197 = 10x

Now divide 10 on both sides to isolate the variable x.

197/10 = 10x/10

19.7 = x

Once you find the value of x, you can check your answer by inputting x back into the original equation.

A+B+C = 180

19.7 + 5(19.7) + 4(19.7) - 17 = 180

19.7 + 98.5 + 61.8 = 180

180 = 180

Therefore the answer for x, or m < A is 19.7 degrees.

Hope this helps :)