Question

Please help with #6 and #7 !!! desperate :(

Answer 1

Answer:

6. X=6

7. x=16 and y=11

Step-by-step explanation:

6. If UW bisects angles m<TUW=(13x-5) and m<WUV=(7x+31), find the value of x

To solve we need set both equations equal to each other

13x-5=7x+31

now we need to get both constants (numbers with out variables for example: 1) alone on one side and Variables alone on one side.

you want to look at the equation and see which one is easier to do first. I see that the most easiest way is to move -5 to the left side. to do so we need to add 5 to both sides.

13x-5=7x+31

+5 +5

13x=7x+3+5

Add 31 and 5 together since there both constants

31+5=36

13x=7x+36

now we need to move 7x to the right side. to do so we need to subtract 7x on both sides.

13x=7x+36

-7x -7x

13x-7x=36

now we need to subtract 7x from 13x since they are liked terms

13x-7x= 6x

6x=36

now we need to isolate x To do so we need to divide by 6 on both sides.

6x=36

--- ---

6 6

x=6

If m<DEG=(5x-4), m<DEF(7x-8)m< DEH=(9y+5) find the values of x and y

Since DEF and DEG are congruent we can add then together to get our x value

congruent angles add up to 180

5x-4+7x-8=180

add 5x and 7x

add -4 and -8

12x-12=180

ISOLATE X

Add 12 on both sides

12x=192

now we need to divide 12 on both sides

12x/12= x

192/12=16

x=16

DEF AND DEH are Vertical opposite meaning they add up to each other. they both have the same degree.

so

9y+5=7x-8

PLUG IN X=16

9y+5=7(16)-8

7*16=112

112-8 =104

9y+5=104

ISOLATE VARIABLE Y

subtract 5 on both sides

9y=99

now divide by 9 on both sides

9y/9=y

99/9=11

y=11