one angle of a parallelogram is 30 dgree more than its adajacent angle ..how much does each measures..
In a parallogram, any two adjacent angles must add up to 180°
so x + x+30 = 180
continue ....
75
To find the measures of the angles in a parallelogram, we need to use the fact that opposite angles in a parallelogram are congruent.
Let's assume that one of the angles in the parallelogram measures x degrees. According to the given information, the adjacent angle to this angle will measure 30 degrees less, which means it will measure (x - 30) degrees.
The opposite angles in a parallelogram are congruent, so the opposite angle to the angle that measures x degrees will also measure x degrees.
Therefore, we have the following angles:
- One angle measures x degrees
- The adjacent angle measures (x - 30) degrees
- The opposite angle to the angle measuring x degrees also measures x degrees
- The opposite angle to the angle measuring (x - 30) degrees also measures (x - 30) degrees
Since the sum of angles in a parallelogram is 360 degrees, we can use this information to set up an equation:
x + (x - 30) + x + (x - 30) = 360
Simplifying the equation:
4x - 60 = 360
Adding 60 to both sides:
4x = 420
Dividing both sides by 4:
x = 105
Now we can substitute this value back into our angles:
- The angle measuring x degrees = 105 degrees
- The adjacent angle = 105 - 30 = 75 degrees
- The opposite angle to the angle measuring 105 degrees = 105 degrees
- The opposite angle to the angle measuring 75 degrees = 75 degrees
Therefore, the measures of the angles in the parallelogram are:
- One angle measures 105 degrees
- The adjacent angle measures 75 degrees
- The opposite angle to the angle measuring 105 degrees also measures 105 degrees
- The opposite angle to the angle measuring 75 degrees also measures 75 degrees