Answer:
According to the Triangle Sum Theorem, any triangles angles add up to 180°
To find the measurement of all angles of any polygon, the formula is:
(number of sides - 2) * 180
However, this cant apply to triangles as we already know it is one triangle with a total angle measurement of 180°. Hence, the formula can't be applied to a triangle. Take a look at the result below when the formula is applied to a triangle:
(3 sides - 2) * 180 = 1 * 180 = 180°
Nothing new. Therefore, for one to find one angle in a triangle, they must:
Add the given angles, then subtract the sum of the given angles from 180.
If all angle measurements are given, but only the variables are supposed to be "known", then you should add all the given angle measurements and put it in an equation like this:
*sum of all the angle measurements* = 180
Thats is, only when you need to know the variable (with the three given angle measurements).
Now, why did we put that "180"?
Because we already have the 3 angle measurements, which undoubtedly equal a 180°.
If your good at solving equations with variables, this should be easy for you. For some others, it may not be. In that case, you can understand the formula and write the equation down on a calculator and get the result.
Back to the question, we'll apply the formula above on this exercise.
4x - 7 + 5x - 3 + x = 180°
1) Combine the like terms *4x, 5x, x* and *-7 - 3*:
4x + 5x + x = 10x
-7 - 3 = -10
2) Simplify the equation:
10x - 10 = 180°
Get rid of anything surrounding the variable (anything you do on one side of the equation shall be done on the other):
- Add +10 on both sides to get rid of whats beside 10x:
10x - 10 = 180°
+ 10 + 10
So the equation looks like this:
10x = 190°
Do the inverse operation; divide 10 on both sides of the equation to get rid of whats beside the 'x':
10x / 10 = 190° / 10
(10 divided by 10 give me nothing, so we have 'x' alone now. 190 divided by 10 equals 19)
x = 19°
Substitute 19 rn and you get the results:
Hope I helped!