In the figure below, the measure of angel 1=3x, the measure of angel 2=y, and the measure of angel 3=72. Find the value of each variable.
Without Visual Examination, we may infer that Angle 1 and Angle 2 are complementary angles (adding up to 90 degrees), because both angles together with Angle 3 form a straight angle (180 degrees in total). Thus, we can express this relationship as:
Angle 1 + Angle 2 = 90 degrees.
Since Angle 1 = 3x and Angle 2 = y, we substitute these values in:
3x + y = 90.
Now, we need to use the given information about Angle 3, which is 72 degrees. We will express another relationship between Angle 1 and Angle 3:
Angle 1 + Angle 3 = 180 degrees.
Substituting Angle 1 = 3x and Angle 3 = 72 degrees, we get:
3x + 72 = 180.
Now, we can solve this system of equations:
3x + y = 90.
3x + 72 = 180.
Subtracting the first equation from the second to eliminate the variable "x", we get:
(3x + 72) - (3x + y) = 180 - 90,
72 - y = 90,
-y = 18,
y = -18.
Now, we substitute this value back into the first equation to find "x":
3x + (-18) = 90,
3x = 90 + 18,
3x = 108,
x = 108/3,
x = 36.
Therefore, the value of x is 36 and the value of y is -18.