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Please help me with the questions http://www.hart.k12.ky.us/userfiles/1064/Classes/8165/Angle%20Addition%20Postulate%20%20Segment%20Addition%20Postulate.pdf

 Oct 1, 2019
 #1
avatar+104969 
+2

Here's a few

 

1) Just  add the measures of  angles LMT  and TMN  to get the measure of angle LMN

 

2) GHQ + QHI   = GHI....so

(29 + x) +( x + 162) =  173

2x + 191  = 173    subtract 191 from each side

2x  = -18        divide both sides by 2

x = -9 

 

3) TMN + LMT  = LMN

     (x + 72)  + (96 + x)  =  166

        2x  +  168 =  166

         2x  = -2

           x  = -1

So LMT  =  96 - 2  =  94°

 

4) Not too much to this one

7 + ?  =  8

 

 

cool cool cool

 Oct 1, 2019
 #2
avatar+104969 
+2

5)  (2x - 4) + (2x - 7)  =   17

I'll let you finish this one

 

6) (x + 14) + (x + 14)  = 12

And this one, too

 

 

 

cool cool cool

 Oct 1, 2019
 #3
avatar+104969 
+2

7)  IJ  = GJ - GI

     IJ  = (x + 27)  - 6

    IJ =    x + 21

 

GJ - HJ  = GH

(x + 27) - (x + 24)  = GH

              3  = GH

 

So....

GH + HI + IJ  = GJ

3 + (2x + 25) + (x + 21)  =  x + 27

3x + 49  =  x + 27

2x  = 27 - 49

2x = -22

x = -11

 

So

 

HJ  =  HI + IJ

HJ = ( 2x + 25) + (x + 21)

HJ =  (2(-11)+25) + (-11 + 21)

HJ = (-22 + 25) + (10)

HJ =  3 + 10

HJ  = 13

 

cool cool cool

 Oct 1, 2019
 #4
avatar+104969 
+1

8) AC  = 15         BD  = 16      AD  = 19

 

We can find BC  [ the overlap of  AC and BD ]   thusly

 

AC + BD  =  15 + 16  = 31

 

BC =  31 - AD

 

BC  = 31 - 19

 

BC  =  12

 

So   AB  =  3   and  CD  = 4

 

Proof

 

A    B        C       D

   3      12      4

 

AC = 15

BD = 16

AD = 19

 

 

   cool cool cool

 Oct 1, 2019
 #5
avatar+2417 
+1

Good job, CPhill!

CalculatorUser  Oct 1, 2019
 #7
avatar+104969 
0

Thanks, CU   !!!!

 

 

 

cool cool cool

CPhill  Oct 2, 2019
 #6
avatar+104969 
+2

9)  AB   = 2x + 30

     BC = 5

     CD  = 8

 

So

 

AB  + BC + CD  =  AD

 

(2x + 30)  + 5 + 8  =  x + 32

 

2x + 43  = x + 32

 

x  = 32 - 43

 

x = -11

 

 

cool cool cool

 Oct 2, 2019
edited by CPhill  Oct 2, 2019
edited by CPhill  Oct 2, 2019
 #8
avatar+104969 
+2

Last one

 

BD  = x + 29

AD  =  x + 39

AC   =  20

BC  = x + 19

 

 

If  AD  =  x + 39   and  BD  = x + 29, then 

AB  =  AD - BD

AB  =  (x + 39) - ( x + 29)

AB  = 10

 

Then

 

AB + BC  =  AC

10 + (x + 19)  = 20

29 + x  =  20

x   = -9

 

Then BC  =  x + 19  =  -9 + 19   =  10

 

Proof

 

A        B        C          D

   10       10       10

 

AC  = 20

BD  = x + 29  =  -9 + 29  =  20

AD =  x + 39  = -9 + 39  = 30

 

cool cool cool

 Oct 2, 2019

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