One of the angles of a parallelogram is 36° greater then another one. Find the angles of the parallelogram.
Let's denote one of the angles of the parallelogram as "x". Since one of the angles is 36° greater than another one, we can express the second angle as "x + 36°".
In a parallelogram, opposite angles are equal. Therefore, the other two angles of the parallelogram will also be "x" and "x + 36°".
To find the measure of the angles, we know that the sum of all the angles in a parallelogram is 360°.
So, we can set up the following equation:
x + (x + 36°) + x + (x + 36°) = 360°
Simplifying the equation, we get:
4x + 72° = 360°
Subtracting 72° from both sides:
4x = 360° - 72°
4x = 288°
Dividing both sides by 4:
x = 288° / 4
x = 72°
Now, substituting the value of x back into our expression for the angles, we can find the measures of all the angles:
Angle 1 = x = 72°
Angle 2 = x + 36° = 72° + 36° = 108°
Angle 3 = x = 72°
Angle 4 = x + 36° = 72° + 36° = 108°
Therefore, the angles of the parallelogram are 72°, 108°, 72°, and 108°.
To find the angles of a parallelogram, we first need to know the relationship between the angles. In a parallelogram, opposite angles are congruent (meaning they have the same measure).
Let's assume one of the angles is x degrees. According to the problem, another angle is 36 degrees greater than x. Therefore, the second angle can be represented as (x + 36) degrees.
Since opposite angles in a parallelogram are congruent, we know that the sum of these two angles is equal to 180 degrees. So, we can write an equation:
x + (x + 36) = 180
Simplifying the equation:
2x + 36 = 180
Subtracting 36 from both sides:
2x = 144
Dividing both sides by 2:
x = 72
Now that we have the value of x, we can find the measures of the angles:
First angle: x = 72 degrees
Second angle: x + 36 = 72 + 36 = 108 degrees
Therefore, the angles of the parallelogram are 72 degrees and 108 degrees.