For the parallelogram, if m∠2 = 5x − 28 and m∠4 = 3x −10 , find m∠3

In a parallelogram, opposite angles are equal. Therefore, m∠2 = m∠4.

Given that m∠2 = 5x - 28 and m∠4 = 3x - 10, we can set these two expressions equal to each other and solve for x:

5x - 28 = 3x - 10

Subtract 3x from both sides to get:

2x - 28 = -10

Add 28 to both sides to get:

2x = 18

Divide both sides by 2 to solve for x:

x = 9

Now that we have the value of x, we can substitute it back into the expression for m∠2 or m∠4 to find the measure of the angle. Let's use m∠2:

m∠2 = 5x - 28 = 5(9) - 28 = 45 - 28 = 17

Therefore, m∠3 = m∠2 = 17 degrees.

In a parallelogram, opposite angles are equal. Therefore, m∠2 = m∠4.

Given that m∠2 = 5x - 28 and m∠4 = 3x - 10, we can set up the equation 5x - 28 = 3x - 10.

Solving for x, we get:

5x - 3x = 28 + 10 2x = 38 x = 19

Substitute x = 19 into the equation for m∠2 to find the measure of angle 2 (which is the same as the measure of angle 4, since they are opposite angles in a parallelogram):

m∠2 = 5(19) - 28 = 95 - 28 = 67 degrees

Therefore, m∠3 = m∠2 = 67 degrees.