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# Geometry

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Oct 1, 2019

#1
+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   Oct 1, 2019
#2
+2

5)  (2x - 4) + (2x - 7)  =   17

I'll let you finish this one

6) (x + 14) + (x + 14)  = 12

And this one, too   Oct 1, 2019
#3
+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   Oct 1, 2019
#4
+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 - 19

BC  =  12

So   AB  =  3   and  CD  = 4

Proof

A    B        C       D

3      12      4

AC = 15

BD = 16   Oct 1, 2019
#5
+1

Good job, CPhill!

CalculatorUser  Oct 1, 2019
#7
0

Thanks, CU   !!!!   CPhill  Oct 2, 2019
#6
+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   Oct 2, 2019
edited by CPhill  Oct 2, 2019
edited by CPhill  Oct 2, 2019
#8
+2

Last one

BD  = x + 29

AC   =  20

BC  = x + 19

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

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   Oct 2, 2019