the adjacent angles of a parallelogram are (3x-12) and52+2x). find the angles of the parallelogram?
To find the angles of a parallelogram, we need to determine the values of the adjacent angles. In this case, the adjacent angles are given as (3x - 12) and (52 + 2x).
Since opposite angles of a parallelogram are equal, we can set these adjacent angles equal to each other.
(3x - 12) = (52 + 2x)
Now, let's solve for x:
3x - 12 = 52 + 2x
First, let's get rid of the variable terms on one side of the equation by subtracting 2x from both sides:
3x - 2x - 12 = 52 + 2x - 2x
Simplifying:
x - 12 = 52
Next, let's isolate the variable x by adding 12 to both sides of the equation:
x - 12 + 12 = 52 + 12
Simplifying:
x = 64
Now that we have the value of x, we can substitute it back into the original expressions to find the angles:
First angle: (3x - 12)
Substituting x = 64:
(3(64) - 12) = 192 - 12 = 180 degrees
Second angle: (52 + 2x)
Substituting x = 64:
(52 + 2(64)) = 52 + 128 = 180 degrees
Therefore, the angles of the parallelogram are both 180 degrees.
Adjacent angles of a parallelogram must add up to 180°
Can you take it from there?