00:01
In this problem, we're asked to find the measures of three angles in a triangle.
00:04
If we know certain conditions, we're told that the second and third angles, or the sum of the second and third angle is equal to five times the first angle, and the third angle is equal to 24 more than the second angle.
00:18
So we're letting x stand for our first angle, y stand for a second angle, and z represents our third angle.
00:24
So we want to try to get two equations with two unknown.
00:27
So we're going to take this z equals y plus 24.
00:30
And we're going to substitute that in where we see z in the first equation.
00:36
So we have x plus y plus y plus 24 equals 180.
00:46
Simplify that.
00:47
We get x plus 2y equals 156.
00:51
Now we're going to take the z equals y plus 24 and substitute the y plus 24 into the second equation.
00:58
So we've got y plus z equals 5.
01:02
But we're going to write y plus y plus 24 equals 5x putting that in standard form we have negative 5x plus 2y equals negative 24 so let's put those two equations together x plus 2y equals 156 and negative 5x plus 2y equals negative 24 so that's our system we're going to solve for x and y let's use the limit method.
01:36
So we're going to multiply that bottom equation by negative 1.
01:41
So the first one stays x plus 2y equals 156.
01:46
The bottom one becomes 5x minus 2y equals negative positive 24...