angle R & angle S are complementary angles..and angle U & and angle V are also complementary angles. if angle R = y-2, angle S = 2x + 3, angle U = 2x-y, and angle V = x-1, find the values of x, y, angle R, S, U, & V
To find the values of x, y, angle R, angle S, angle U, and angle V, we can use the information that angle R and angle S are complementary, and angle U and angle V are also complementary.
Complementary angles add up to 90 degrees.
Angle R + Angle S = 90 degrees.
Therefore, (y-2) + (2x + 3) = 90.
Angle U + Angle V = 90 degrees.
Therefore, (2x-y) + (x-1) = 90.
Let's solve these equations to find the values of x and y:
1. (y-2) + (2x + 3) = 90
Simplifying the equation:
2x + y + 1 = 90
2x + y = 89 ..... Equation 1
2. (2x-y) + (x-1) = 90
Simplifying the equation:
3x - y - 1 = 90
3x - y = 91 ..... Equation 2
Now we can solve these simultaneous equations using the method of substitution:
From Equation 1, we can express y in terms of x:
y = 89 - 2x
Substituting the value of y in Equation 2:
3x - (89 - 2x) = 91
3x - 89 + 2x = 91
5x - 89 = 91
5x = 180
x = 36
Now substituting the value of x in equation 1:
2(36) + y = 89
y = 17
So, the values of x and y are x = 36 and y = 17 respectively.
Plugging these values back into the given angle expressions, we find:
Angle R = y - 2 = 17 - 2 = 15
Angle S = 2x + 3 = 2(36) + 3 = 75
Angle U = 2x - y = 2(36) - 17 = 55
Angle V = x - 1 = 36 - 1 = 35
Therefore, the values are:
x = 36
y = 17
Angle R = 15 degrees
Angle S = 75 degrees
Angle U = 55 degrees
Angle V = 35 degrees
To find the values of x, y, angle R, angle S, angle U, and angle V, we need to use the information that angle R and angle S are complementary, and angle U and angle V are also complementary.
Complementary angles are two angles whose sum is 90 degrees.
We have the following equations for the angles:
angle R = y - 2
angle S = 2x + 3
angle U = 2x - y
angle V = x - 1
Since angle R and angle S are complementary, we can set up the equation:
angle R + angle S = 90
Substituting the values we have for angle R and angle S:
(y - 2) + (2x + 3) = 90
Simplifying the equation:
y + 2x + 1 = 90
y + 2x = 89 ----(1)
Similarly, since angle U and angle V are complementary, we can set up the equation:
angle U + angle V = 90
Substituting the values we have for angle U and angle V:
(2x - y) + (x - 1) = 90
Simplifying the equation:
3x - y - 1 = 90
3x - y = 91 ----(2)
Now, we have two equations (1) and (2) with two variables (x and y). We can solve these equations simultaneously to find the values of x and y.
We can use the method of substitution or elimination to solve these equations.
Let's use the method of substitution:
From equation (1), we can express y in terms of x:
y = 89 - 2x
Substituting this value of y in equation (2):
3x - (89 - 2x) = 91
Simplifying the equation:
3x - 89 + 2x = 91
5x - 89 = 91
5x = 180
x = 36
Now substituting the value of x in equation (1):
y + 2(36) = 89
y + 72 = 89
y = 17
Thus, we have found the values of x and y:
x = 36
y = 17
Now, we can substitute these values of x and y back into the equations for the angles to find their values:
angle R = y - 2 = 17 - 2 = 15
angle S = 2x + 3 = 2(36) + 3 = 75
angle U = 2x - y = 2(36) - 17 = 55
angle V = x - 1 = 36 - 1 = 35
Therefore, the values of x, y, angle R, angle S, angle U, and angle V are:
x = 36
y = 17
angle R = 15
angle S = 75
angle U = 55
angle V = 35