Answer / Step-by-step explanation:
In a parallelogram, opposite angles are equal in measure. Therefore, we can add the first two angles together and the last two angles together, and set them equal to each other to form an equation:
2x + 3x = 2y + 3y
Simplifying the equation, we get:
5x = 5y
Dividing both sides by 5, we get:
x = y
This means that the first and third angles are equal in measure, and the second and fourth angles are equal in measure.
Let's call each angle "a" and solve for it.
From the given ratio, we know that:
2x = 2a
3x = 3a
We can use the second equation to In a parallelogram, opposite angles are equal in measure. Therefore, we can add the first two angles together and the last two angles together, and set them equal to each other to form an equation:
2x + 3x = 2y + 3y
Simplifying the equation, we get:
5x = 5y
Dividing both sides by 5, we get:
x = y
This means that the first and third angles are equal in measure, and the second and fourth angles are equal in measure.
Let's call each angle "a" and solve for it.
From the given ratio, we know that:
2x = 2a
3x = 3a
We can use the second equation to solve for x:
3x = 3a
x = a
Substituting x = a into the first equation, we get:
2a = 2a
This confirms that the first and third angles are equal in measure, and the second and fourth angles are equal in measure.
Therefore, each angle in the parallelogram has a measure of:
2x = 2a = 2(180 - 3a) = 360 - 6a
3x = 3a = 3(180 - 2a) = 540 - 6a
Simplifying these expressions, we get:
Each of the first and third angles has a measure of 120 degrees, and each of the second and fourth angles has a measure of 180 - 120 = 60 degrees.
for x:
3x = 3a
x = a
Substituting x = a into the first equation, we get:
2a = 2a
This confirms that the first and third angles are equal in measure, and the second and fourth angles are equal in measure.
Therefore, each angle in the parallelogram has a measure of:
2x = 2a = 2(180 - 3a) = 360 - 6a
3x = 3a = 3(180 - 2a) = 540 - 6a
Simplifying these expressions, we get:
Each of the first and third angles has a measure of 120 degrees, and each of the second and fourth angles has a measure of 180 - 120 = 60 degrees.