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