Answer:
6. X=6
7. x=16 and y=11
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