Two angles are complemtary. The large angle is 1 less than 6 times the smaller angle. which system could be used to determine the larger angle X and the smaller angle Y?
Let X be the larger angle and Y the smaller. Your system of two equations is:
X + Y = 90 (degrees)
X = 6Y - 1
7Y - 1 = 90
7Y = 91
Y = 13
X = 90 - 13 = 77
To determine the larger angle (X) and the smaller angle (Y), we can set up a system of equations based on the given information.
Let's assume that the smaller angle is Y degrees. Therefore, the larger angle would be 6Y - 1 degrees, as it is stated that the larger angle is 1 less than 6 times the smaller angle.
Now, as the two angles are complementary, their sum should be 90 degrees. So we can set up the following equation:
X + Y = 90
Substituting the value of X from the previous equation:
(6Y - 1) + Y = 90
Simplifying the equation:
7Y - 1 = 90
Adding 1 to both sides:
7Y = 91
Dividing both sides by 7:
Y = 13
Now, we have found the value of the smaller angle (Y) to be 13 degrees. To find the larger angle (X), we substitute this value back into the expression we found earlier:
X = 6Y - 1
X = 6(13) - 1
X = 78 - 1
X = 77
Hence, the system of equations to determine the larger angle (X) and the smaller angle (Y) is:
X + Y = 90
X = 6Y - 1
The solution is X = 77 degrees and Y = 13 degrees.