if an angle of parallelogram is two third of its adjacent angle,find the angles of the parallelogram
To find the angles of a parallelogram, we first need to understand the relationship between its angles.
In a parallelogram, opposite angles are congruent (they have the same measure). Therefore, if we know one angle, we can find another angle by simply subtracting the known angle from 180 degrees.
Let's call the measure of one angle in the parallelogram x degrees. According to the given information, the measure of the adjacent angle is two-thirds of x. Therefore, the measure of the adjacent angle can be represented as (2/3)x degrees.
Since opposite angles in a parallelogram are congruent, the angle opposite to x degrees will also measure x degrees.
Now, since opposite angles sum up to 180 degrees, we can set up the following equation:
x + (2/3)x + x + (2/3)x = 180
Combining like terms:
2x + (4/3)x = 180
Multiplying both sides by the least common multiple (3) to eliminate the fraction:
6x + 4x = 540
10x = 540
Dividing both sides by 10:
x = 54
Now, we know that one angle in the parallelogram measures 54 degrees. Using this information, we can find the measures of other angles:
The adjacent angle measures (2/3) * 54 = 36 degrees.
The opposite angle measures 54 degrees.
And finally, the adjacent angle to the opposite angle measures (2/3) * 54 = 36 degrees.
Therefore, the angles of the parallelogram are: 54 degrees, 36 degrees, 54 degrees, and 36 degrees.