Answer:
Explanation:
You should note:
- A parallelogram's total angles add up to 360 degrees
- Opposite angles within a parallelogram are equivalent
--> which means that 123 degrees = 3y degrees, and (2x - 5) degrees = the unmarked angle's degrees
To solve for the top left corner:
3y = 123, divide both sides by 3
y = 41; the top left angle is 123 degrees
To solve for the bottom left corner:
You already know that two of the angles (the top left and bottom right) are 123 degrees, and that all the angles in the parallelogram add up to 360 degrees. So to solve for the remaining degrees of the (2x - 5) angle and the unmarked angle, you'd do -->
360 - 2(123) =
360 - 246 =
114 degrees
114 degrees is the combined degrees of the top right angle and bottom left angle, so divide it by 2 to find the degrees of one of those angles -->
114/2 = 57 degrees
You can use this value to find x, as well as to note that the top right angle is 57 degrees -->
(2x - 5) = 57, add 5 to both sides
2x = 62, divide both sides by 2
x = 31; the bottom left angle is 57 degrees.
To check:
Add all the known angles up with the known variable values -->
[3(41)] + 57 + [2(31) - 5] + 123 = 360 degrees
123 + 57 + (62 - 5) + 123 = 360 degrees
307 + 57 = 360 degrees
360 degrees = 360 degrees
Overall:
The top left and bottom right angles are 123 degrees, the top right and bottom left angles are 57 degrees, y = 41, and x = 31.