Find the sum of the angle measures

Question

Use the diagram to find the angle measures of the triangle. Recall that the sum of the angle measures of a triangle is 180 degrees. X degree= (X+4)degree = 6x degree=

(didn’t know how to put the degree symbol) but they equal what degree? I’m unsure how to solve this!

Answer 1

Hi there!

So, for this question, we know that the sum of the angles in the triangle must equal 180°, and each of these expressions is equal to one of the angles in the triangle. Since we know that these three angles must add up to 180, we can then combine them into one sum:

x + (x + 4) + 6x = 180

If we remove the parentheses and combine like terms, we then have:

1) x + x + 4 + 6x = 180

2) 2x + 4 + 6x = 180

3) 8x + 4 = 180

From here, we can then perform some simple algebra to solve for x:

1) 8x + 4 = 180

2) 8x = 176

3) x = 22

Once we have this value, though, remember that we're not done! Each of the angles is an expression in terms of x, so we then have to solve for each equation and substitute x = 22:

First angle:

x = 22

Simple enough, the first angle is 22°.

Second angle:

1) x + 4 = 2nd angle

2) 22 + 4 = 26

So we get the second angle is 26°.

Third angle:

1) 6x = 3rd angle

2) 6(22) = 6 * 22 = 132

So we solve that the third angle is 132°.

A simple way to check if these answers are correct is to see if they all add up to be 180°, since it can't be a triangle otherwise:

1st angle = 22

2nd angle = 26

3rd angle = 132

22 + 26 + 132 = 180

Sure enough, it does! So there we have our angles. I hope this helped and gave a feel for how one should approach these kinds of problems.