In Parallelogram PARK,
angle P = (7x) degree
angle A = (3x - 20) degree
angle K = (5y - 10) degree.
What is x + y?
opposite angles are equal, and consecutive angles are supplementary, so
3x-20 = 5y-10
7x + 3x-20 = 180
x+y = 30
In a parallelogram, opposite angles are equal. Therefore, angle P = angle K.
Given, angle P = (7x) degrees and angle K = (5y - 10) degrees.
Setting them equal:
7x = 5y - 10
Let's solve for x:
7x + 10 = 5y
7x = 5y - 10
Since we know that angle A = (3x - 20) degrees, we can substitute the value of x into this equation:
A = 3x - 20
A = 3(5y - 10) - 20
A = 15y - 30 - 20
A = 15y - 50
Since P = K, we have:
7x = 5y - 10
We can equate it to angle A:
7x = 15y - 50
Now, we have a system of equations:
7x = 5y - 10 (Equation 1)
7x = 15y - 50 (Equation 2)
Subtracting Equation 1 from Equation 2:
7x - 7x = 15y - 5y - 50 + 10
0 = 10y - 40
Simplifying:
10y = 40
y = 40/10
y = 4
Now, we can substitute the value of y back into Equation 1 to solve for x:
7x = 5(4) - 10
7x = 20 - 10
7x = 10
x = 10/7
So, x = 10/7 and y = 4. To find x + y:
x + y = 10/7 + 4.
Therefore, x + y = 10/7 + 4 = (10 + 28)/7 = 38/7.
To find the value of x + y, we need to use the fact that the sum of the interior angles of a parallelogram is always 360 degrees.
In Parallelogram PARK, we are given the measures of angles P, A, and K as follows:
Angle P = 7x degrees
Angle A = (3x - 20) degrees
Angle K = (5y - 10) degrees
Since we know that the sum of the interior angles of a parallelogram is 360 degrees, we can write the equation:
Angle P + Angle A + Angle R + Angle K = 360 degrees
Substituting the given angle measurements, we have:
7x + (3x - 20) + R + (5y - 10) = 360
Now, let's simplify the equation:
7x + 3x - 20 + R + 5y - 10 = 360
Combining like terms:
10x - 30 + R + 5y = 360
Now, let's group the terms with x and the terms with y separately:
10x + 5y + R - 30 = 360
From this equation, we can see that the value of x and y are not directly given. We need additional information or equations to solve for x and y.
Therefore, without more information, we cannot determine the value of x + y.