mom2three Posted October 7, 2011 Share Posted October 7, 2011 The soulution guide has this: 32x + 4y=680 3x-y=80 ________________ Where did they get these two equations from? Where did the 680 and 80 come from? I am so rusty with Geometry that I really can't help my son. Thank you to anyone that can help. Quote Link to comment Share on other sites More sharing options...
MyThreeSons Posted October 7, 2011 Share Posted October 7, 2011 I don't have Chalkdust, so I can't look it up. I know, though, that it can be difficult to post a Geometry problem, especially if it is given in the form of a diagram. Quote Link to comment Share on other sites More sharing options...
creekland Posted October 7, 2011 Share Posted October 7, 2011 Is there any way you can post the question even if you have to describe it? We never did Chalkdust Geometry. Quote Link to comment Share on other sites More sharing options...
blossom12 Posted October 7, 2011 Share Posted October 7, 2011 Don't forget if you are the original purchaser of the Chalkdust program you have complete access to emailing Uncle Buck. He is very prompt in getting back to you. blossom12 Quote Link to comment Share on other sites More sharing options...
mom2three Posted October 10, 2011 Author Share Posted October 10, 2011 the picture is a parallelogram with corners, A, B, C, D. Given: DC//AB Angle A is congruent to Angle C Angle A=3x+y Angle D=5x+10 Angle C= 5y+20 Find Angle B Thanks. Quote Link to comment Share on other sites More sharing options...
MyThreeSons Posted October 10, 2011 Share Posted October 10, 2011 the picture is a parallelogram with corners, A, B, C, D. Given: DC//AB Angle A is congruent to Angle C Angle A=3x+y Angle D=5x+10 Angle C= 5y+20 Find Angle B Thanks. Assuming that, at this point, you've been taught about parallel lines cut by a transversal, the following relationships will be true: 1. Angle A is congruent to Angle C (they didn't need to tell you that once they told you ABCD was a parallelogram) 2. Angle D is congruent to Angle B 3. Each pair of consecutive angles is supplementary (they add up to 180 degrees) From 3 above, we know that Angle A + Angle D = 180: 3x + y + 5x + 10 = 180 combine like terms 8x + y + 10 = 180 subtract 10 from both sides 8x + y = 170 multiply both sides times 4 (why this step is a mystery to me) 32x + 4y = 680 --this is your first equation from the solution similarly, Angle D + Angle C = 180: 5x + 10 + 5y + 20 = 180 5x + 5y + 30 = 180 5x + 5y = 150 x + y = 30 From this point, I would use the two equations (8x + y = 170 and x + y = 30) to solve for x and y. When I do that, I get x = 20 and y =10. Since Angle B is congruent to Angle D, Angle B would be 110 degrees. The second equation you posted in the solution (3x - y = 80) must be a mistake. It simply doesn't fit with the data of the problem. HTH Quote Link to comment Share on other sites More sharing options...
creekland Posted October 10, 2011 Share Posted October 10, 2011 the picture is a parallelogram with corners, A, B, C, D. Given: DC//AB Angle A is congruent to Angle C Angle A=3x+y Angle D=5x+10 Angle C= 5y+20 Find Angle B Thanks. There are several ways you can solve this including the one given above. I agree that I don't see the second equation they gave (3x - y = 80) coming from this at all. I'm thinking it's a typo and here's why. If you use the fact that A is congruent to (equal to) C then you get: 3x + y = 5y + 20 Combining the "ys" we get: 3x - 4y = 20 This is what I think the second equation is supposed to be. Then if you use A + D = 180 (as in the above equation) you'd have two equations: 3x - 4y = 20 (from A = C) 8x + y = 170 Then I would multiply the second equation by 4 to get the first equation they gave you. 3x - 4y = 20 32x + 4y = 680 Add those together and you get: 35x = 700 and x = 20 (as in the above solution). Any way a student solved this using A = C or C + D =180 and either A + D = 180 or C + D = 180 (if A = C were chosen earlier) or even A + B + C + D = 360 will work to solve for B correctly. The key is you need two equations to solve for two variables (x and y). To get these two equations angles next to each other in a parallelogram add up to 180 and angles across from each other are congruent/equal. Quote Link to comment Share on other sites More sharing options...
MyThreeSons Posted October 10, 2011 Share Posted October 10, 2011 I agree that I don't see the second equation they gave (3x - y = 80) coming from this at all. I'm thinking it's a typo Thank you. I typed my answer early this morning after very little sleep, then was gone all day. In the back of my mind, I was afraid that I had made a silly mistake and would be sheepishly apologizing. It's great to be able to double-check such things with one another. Quote Link to comment Share on other sites More sharing options...
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