In the parallelogram below, if angle B=2x+15 and angle A=3x-5, what is the measure of angle D?

as of connections academy 2020 the answers for parallel and perpendicular lines unit test are

1. a
2. c
3. c
4. c
5. c
6. b
7. d
8. d
9. c
10. c
11. b
12. d

To find the measure of angle D in the parallelogram, we need to use the property that the opposite angles in a parallelogram are equal.

In this case, angle B is opposite to angle D and angle A is opposite to angle C.

So, we can set up the equation:

angle B = angle D

2x + 15 = angle D

Now, we need to find the value of x.

We can also set up another equation using the fact that the sum of the angles in a parallelogram is 360 degrees:

angle A + angle B + angle C + angle D = 360 degrees

Substituting the given values:

(3x - 5) + (2x + 15) + angle C + (2x + 15) = 360

Combine like terms:

5x + 25 + angle C + angle C = 360

Now, let's solve this equation for x:

5x + 25 + 2(angle C) = 360

5x + 25 + 2(angle C) - 25 = 360 - 25

5x + 2(angle C) = 335

Now, we can substitute the value of x back into our equation for angle D:

2x + 15 = angle D

2(x) + 15 = angle D

2(335) + 15 = angle D

670 + 15 = angle D

685 = angle D

So, the measure of angle D is 685 degrees.

To find the measure of angle D in the parallelogram, we need to use the fact that opposite angles in a parallelogram are congruent.

In this case, angle B and angle D are opposite angles, so they must be equal. Therefore, we can set up the following equation:

angle B = angle D

2x + 15 = angle D

Now, we also know that the sum of the angles in a parallelogram is 360 degrees. Since angle A and angle B are consecutive angles in the parallelogram, their sum must be 180 degrees. Therefore, we can set up another equation:

angle A + angle B = 180

3x - 5 + (2x + 15) = 180

Simplifying the equation:

5x + 10 = 180

Subtracting 10 from both sides:

5x = 170

Now, divide both sides by 5 to solve for x:

x = 34

Now, substitute the value of x back into the first equation to find the measure of angle D:

angle D = 2x + 15

angle D = 2(34) + 15

angle D = 68 + 15

angle D = 83

So, the measure of angle D in the parallelogram is 83 degrees.

well, A+B=180, so solve for x.

Also, A+D = 180