For what values of the variables must ABCD be a parallelogram?

Answers

Answer 1

Answer: okfirst things first. In all parallelograms, you now that opposite anglesare numerically equal to each other and that the sum off all fourangles must add up to 360.

Therefore based off the picture, angles B and D are equal to each other, and A and C are equal to each other.

(2x-10) = (y+20) B = D
y=2x-30

Now B = 2x -10 and D = 2x-30+20 = 2x-10

Now A = C

Since A = 2x+ 10, we can assume C = 2x + 10

Now we need to find the value of x

so our angle A, B, C, and D add up to 360 so the "master equation" is:

(2x - 10) + (2x - 30 + 20) + (2x + 10) + (2x + 10) = 360
2(2x -10) + 2(2x + 10) = 360
4x - 20 + 4x + 20 = 360
8x = 360
x = 45

Now that we know what x is, we can go back to the angles B and D

remember B = 2x - 10 and D = y + 20

and earlier we stated that y=2x-30
therefore y = 2(45) - 30
Y = 60

Now if you wanted to double check, all you have to do is plug in the xand y values into the equations and add up all the angles together andthey should add up to 360.

I know I kinda went into too many details, but I'd rather explain itinto too much detail rather than too few details and shortcuts that youwouldn't be able to follow and understand.

I hope this was helpful =D

Answer 2

Answer:

Final answer:

ABCD is a parallelogram if either both pairs of opposite sides are parallel, both pairs of opposite sides are equal, or one pair of opposite sides is both parallel and equal.

Explanation:

In mathematics, a quadrilateral ABCD is considered a parallelogram if it meets one of these three conditions:

Both pairs of opposite sides are parallel (AB || DC and AD || BC).
Both pairs of opposite sides are equal (AB = DC and AD = BC).
One pair of opposite sides is both parallel and equal (AB = DC and AB || DC).

So, the values of the variables you have in your problem have to satisfy at least one of these conditions to make ABCD a parallelogram.

Learn more about Parallelogram here:

brainly.com/question/31342904

#SPJ3

Related Questions

Find the missing number 32/52= ?/13
Determine whether each expression is equivalent to −9.8+(−4.3).Select Yes or No for each expression. −9.8−4.3 Yes No −9.8+(−0.2)+(−4.1) Yes No −9.8−0.2+4.1 Yes No −9.8+(−0.2−4.5) Yes No −9.8+0.2−4.5 Yes No
Take a look at the figure. What are the coordinates of the point labeled A in the graph shown?A. (2, 2) B. (–2, 4) C. (2, –2) D. (–2, 2)
In the graph of the equation, 2x – 8y = 32, what is the y-intercept (b) of the line? Express the answer as an ordered pair.
In APQR, ZQ = ZP, RP = 13 and PQ = 19. Find the length of QR.

A line crosses the y-axis at (0,4) and has a slope of -2. Find an equation for the this line.A) y = 2x + 4 B) y = -2x + 4 C) y = -2x - 4 D) y = -4x + 2 <-- 6)Write the equation of the line with the given slope and y-intercept.
slope = 5 y-intercept = 8 A) y = 5x + 8 B) x = 5y + 8 <-- C) y = 8x + 5 D) x = 8y + 5

Answers

C) y = -2x -

A) y = 5x + 8

Given that cos42° is simpler to 0.743, What is the sine of the complementary angle?

Answers

The cos of an angle and the sine of its complement are the same number.
Spend a couple of minutes looking at a right triangle, and reviewing the definitions of sin and cos, and you'll see why.

cos(42)=sin(90-42)

So in this case:

cos(42)=sin(48)

As:

A complementary angle is either of two angles whose sum is 90 degrees. {Source: Google}

How Can associative Property be used to mentally find 48+82?

Answers

Associative property of addition represents this equation:
a + b = b + a
So, how would it be helpful with this given equation?
=> 48 + 82
=> Let's start with the ones place value.
(2 + 8) = 10, bring down 0, carry 1 then ( 4 + 8) = 12 + 1 = 13
So the answer is 130.
If we are going to do it vice versa, still expect that the same answer will occur.

A cone has a volume of 12 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of? a. 6 in3
b. 24 in3
c. 36 in3
d. 48 in3

Answers

To find the volume of a cylinder that the cone fits exactly inside, we can use the formula for the volume of a cone. By solving for the radius and height of the cone, we can then substitute those values into the formula for the volume of a cylinder to obtain the volume.The correct option is C.

To find the volume of a cylinder that the cone fits exactly inside, we need to understand the relationship between the cone and the cylinder. The volume of a cone can be found using the formula V = (1/3) * π * r^2 * h, where r is the radius and h is the height of the cone. The volume of the cylinder is equal to the volume of the cone, so the volume of the cylinder can also be calculated using the formula V = π * r^2 * h. In this case, the volume of the cone is given as 12 cubic inches. We can set up an equation to find the radius and height of the cone using this volume, and then use those values to find the volume of the cylinder.

Let's solve for the radius and height of the cone:

1.Start with the formula for the volume of a cone: V = (1/3) * π * r^2 * h

2.Substitute the given volume of the cone as 12 cubic inches: 12 = (1/3) * π * r^2 * h

3.Cancel out the 1/3 by multiplying both sides of the equation by 3: 36 = π * r^2 * h

4.Divide both sides of the equation by π to isolate r^2 * h: r^2 * h = 36/π

5.Since we don't have enough information to solve for both r and h, we will express the height h in terms of the radius r.

6.Substitute r^2 * h with 36/π: r^2 * (36/π) = 36/π

7.Simplify the equation by canceling out the π: r^2 * (36/π) = 36/π

8.Multiply both sides of the equation by π/36: r^2 = 1/π

9.Take the square root of both sides to find the radius r: r = 1/√π

10.Now that we have the radius, we can find the height using the equation r^2 * h = 36/π: (1/√π)^2 * h = 36/π

11.Simplify the equation: h = 36

So, the radius of the cone is 1/√π and the height is 36. Using these values, we can calculate the volume of the cylinder:

1. Start with the formula for the volume of a cylinder: V = π * r^2 * h

2. Substitute the values we found for the cone into the formula: V = π * (1/ √π)^2 * 36

3. Simplify the equation: V = 36 cubic inches

the volume of the cylinder that the cone fits exactly inside is 36 cubic inches.

Therefor the correct option is C.

Learn more about volume of a cone and cylinder here:

brainly.com/question/35498382

#SPJ2

Volume of a cone = 1/3 r² π h
Volume of a cylinder = r² π h = 3 · V ( cone ) = 3 · 12 = 36 in³
Answer: C )

55.04 is what percent of 21.5

Answers

The number 55.04 is 256 % of 256 percentage of the number 21.5

What is Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the percentage be represented as A

Let the first number be represented as p

Now , the value of p = 55.04

Now , the second number is q = 21.5

Now , the percentage of the number 55.04 of 21.50 is given by

p = A % of 21.5

p = ( A / 100 ) x 21.5

Multiply by 100 on both sides , we get

5504 = 21.5A

Divide by 21.5 on both sides , we get

A = 5504 / 21.5

A = 256 %

Therefore , the value of A is 256 %

Hence , the percentage is 256 %

To learn more about percentage click :

brainly.com/question/12861068

#SPJ2

256% is definitely the answer

The data set gives the number of bottles filled by each of the workers in a bottling plant in one day. {36, 18, 16, 28, 68, 35, 37, 66, 38, 40, 41, 44, 72, 29}