figure cdef is a parallelogram. what is the value of r? 2 3 4 5 This is a topic that many people are looking for. bluevelvetrestaurant.com is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, bluevelvetrestaurant.com would like to introduce to you KutaSoftware: Geometry- Properties Of Parallelograms Part 2. Following along are instructions in the video below:
This video. Were continuing on with the properties of parallelograms free worksheet on the the cuda software website. Ill leave a link in the description below so you how to access this geometry worksheet in this next section.
Were solving for x. Given that each figure is a parallelogram and number 11. We can see that angle z and angle y are consecutive angles.
Within a parallelogram and therefore sum to equal 180 degrees. So z plus y. Equals 180.
Degrees z. Is 80 degrees. And y is 11 x.
Minus. 10. And that is equal to 180.
Im going to combine like terms. My 80 and my 1080 minus. 10.
Is 70 so 70 plus 11x equals 180. When i subtract 70 from both sides. Ill get that 11x equals 110.
Dividing by 11. Ill isolate my x. And get that x is equal to 110 divided by 11.
Which is 10 so. 10 is my solution in number 11. And remember if i wanted to solve for this angle.
Y. I would just plug 10 in for x and solve that would give me the measure of angle y and number 12. Were given the length of two opposite sides and opposite sides within a parallelogram are congruent so st is equal to ru st is 2x plus 15.
And thats equal to ru. Which is x plus 15. Ill subtract 15 from both sides and at the same time.
Ill also subtract x. From both sides. 2x minus x.
Is x. And x. Is going to equal 15 minus.
15. Which is 0. So the number 12 x is 0.
And number 13. Im given consecutive angles. You and b therefore theyre supplementary so you plus b.
Equals 180. So im going to take angle u. Which is 9x plus 15 add that to 6x plus.
15. Which is angle v. And thats going to equal 180.
Combining my like terms. Im going to combine 9x 6 x. And im going to combine 15.
And 15. 9x. Plus.
6x. Is. 15 x.
15. 15. Is.
30 15. X. Plus.
30. Equals. 180.
Subtracting. 30. From both sides.
Ill get that 15 x. Is equal to 150.
And then finally when i divide by 15. Ill isolate my x in other words get it all by itself. So ill know that x is equal to 10 since 150.
Divided by 15 is 10. So. 10 is my solution and number 13 and number 14 again i have a consecutive angle.
And i know that was in a parallelogram those are supplementary so i have 35 degrees. Which is s plus t. Which is 14 x.
Plus. 5. And that is going to be equal to 180 since theyre supplementary combining my like terms.
I can combine 35 with 5 to get 40. So 40 plus 14x equals. 180.
Subtracting 40 from both sides. Ill have the 14 x. Equals.
140. My final step is to divide by 14 in doing that ill get that x. Equals.
140. Divided by 14. Which is 10 so x equals.
10. In number 14. And number 15.
Im given opposite sides and i know that opposite sides of a parallelogram are congruent so that means that v w. Is equal to ux vw7 and that is equal to ux. Which is x plus 1.
And in order to solve for x. Ill just subtract by 1 to get that. 6 is equal to x 6.
Is my solution for number 15 and number 16 angle k. Is supplementary with angle j. So 50 x.
Plus 130 x. Will equal 180. Combining my like.
Terms. 50x. Plus.
130. X. Is 180.
X. And that is equal to 1. Under.
80. And i know that 180 divided by itself is equal to 1. So 1 times.
X. Equals. X.
And thats equal to 180. Divided by 180. Which is 1 so for number 16 x.
Is equal to 1 and number 17. Im given the measurement of you h. Which is 19.
Im also given that fh the entire diagonal is 5x minus 7. I know that hu is congruent to you f. Since u.
Is where the diagonals bisect each. Other so you would be my midpoint so hgo is 19 and you at this 19. I also know that f h is u h plus u f so f h equals u h u f.
And if you h equals u f. That means that f h. Which is 5x minus.
7. Equals. 19.
So 5x minus. 7. Equals.
19. Plus. 19.
Which is 38 adding. 7. To both sides.
Ill get that 5x is equal to 45. And when i divide by 5. Ill get that x is equal to 9 and number 17 x is 9.
And number 18. Im given measurements for k u. And um u.
Is the midpoint between k. U. And um.
So k. U. Is equal to um since.
Theyre congruent. So 3. X.
Plus. 3. Is equal to 4 x.
Minus. 4. Ill subtract 3x from both sides to get that.
3. Equals. X.
Minus. 4. And then ill add 4 to both sides and doing that ill get that.
7 is equal to x so. 7. Is the solution in number 18 and for the last four problems on this worksheet.
Im going to find the measure indicated in each parallelogram. So im going to be doing what ive just done in the previous section. However now im going to plug in x to solve for the indicated measurement in 19.
Im finding our q. And i know the rq is congruent to s p. So our q is equal to 3x plus 3.
But since our q is equal to sp. Im going to say that negative 1 plus 4 x is equal to 3x plus. 3.
Ill subtract 3x from both sides to get that x added to negative 1 equals. 3 adding. 1 to both sides.
Ill isolate the x to get that x is equal to a positive. 4. So now im going to take that value of x and plug it in for the x in my equation of our queue.
So thats going to give me 3 times x. Which is 3 times. 4 plus.
3. Which 3 times. 4.
Is 12 plus. 3. Is 15.
So our q is equal to 15 and number 19 and number 20. Im finding the measure of angle g. And we know that the measure of angle g.
Is 5 x minus. 9. And angle g.
Is opposite angle. Eath therefore. They are congruent.
So angle. E.
3x plus. 11. Is equal to angle g of 5x minus.
9. Ill subtract 3x from both sides to get that 11 is equal to 2x minus 9. And when i add 9 to both sides.
Ill get that 20 is equal to 2x so dividing by 2 will give me that 10 is x taking my value of x and plugging it in to my equation for the measure of angle g. Ill get. 5 times x.
Or just. 5. Times.
10. Minus. 9.
5. Times. 10.
Is 50 minus. 9. Is 41.
So 41 degrees. Is the measure of angle g and number 21. Im finding te and te is equal to 4 plus 2 x.
Te is congruent to eb since e. Is the midpoint of t v. So if te equals e v.
That means that te 4 plus 2x is equal to eb 4 x. Minus. 4.
So lets solve for x. Ill subtract 2x from both sides to cancel out my xs on my left. And at the same time.
Ill add 4 to both sides in order to cancel out my terms without x. On the right. 4 plus.
4 is 8 and that is equal to 4x minus 2x. Which is 2x so when i divide by 2 i get that 4 is equal to x so knowing that 4 is x. Im going to plug that in for my equation for te.
Which is this first equation given 4 plus 2x so 4 plus 2x equals 4. Plus 2 times. 4.
Which is 4 plus. 8. And thats equivalent to 12.
So 12 is te and number 21 and if 12 is te evie is also 12 since they are congruent number 22. Were finding the measure of angle ts r. Now its hard to see exactly what which equation goes with it which angle.
But i believe that 2x 14 goes with angle r s u 2 x 7 goes with us t so we can see the measure of angle ts r. Plus the measure of angle t equals 180 degrees. And the measure of angle ts r.
Is the measure of angle r. Su. 2x plus 14 plus ust 2x minus.
7. So if the entire angle tsr equals. 2x plus.
14. Plus. 2x minus.
7. If we add that to the supplementary angle of 125. Thats going to equal 180.
Now were going to combine like terms and solve for x 2x and 2x can be combined together and so can 14 negative. 7. And 125.
2x plus. 2x is 4x. 14.
Minus. 7. Is 7 7.
Equals. 132. So 4x plus.
132. Equals 180. But when we subtract 132 from both sides we get that 4x equals 48.
So dividing both sides by 4. Well get that x is equal to 48 divided by 4 which is 12 now remember the angle. Were looking for is rst or ts r.
Ts. R. Equals 2x plus 14 plus 2x minus 7.
So were going to plug our value of x. Which is 12 in for the x in the equation for the measure of angle ts r. So measure of angle ts.
R. Equals. 2.
Times 12 plus 14 plus. 2. Times.
12. Minus. 7.
Simplifying. This. 2 times.
12. Is. 24.
Plus. 14. Plus.
2. Times. 12.
Which is 24. Minus. 7.
24. Plus. 14.
Plus. 24. Minus.
7. Is going to give us 55. So 55.
Degrees. Is the measure of angle t s. R.
And if you want to double check remember that opposite sides are congruent. So we have that the measure of angle t. 125.
Equals r. So. Thats also 125 and rst or ts r.
Is 55. So. Tu r is awesome.
55. Degrees. And we know that the angles in a quadrilateral add up to 360.
So if we do 125. Plus. 125.
Plus. 55. Plus.
55. That indeed. Equals 360.
And with that final solution. We wrap up this worksheet. If you have any questions leave a comment below and if you havent subscribed go ahead and do so now and like this video.
If you found it useful. .
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