Pentagon RSTUV is circumscribed about a circle. What is the value of x if RS = 10, ST = 13, TU = 11, UV = 12, and VR = 12?

x=6

y=7

z=4

a=8

b=4

Step-by-step explanation:

Let A,B,C,D,E are points on the circle or where RS,ST,TU,UV,VR touches the circle respectively.

RS=RAS=RA+AS=b+x=10

ST=SBT=SB+BT=x+y=13

TU=TCU=TC+CU=y+z=11

UV=UDV=UD +DV=z+a=12

VR=VER= VE +ER=a+b=12

∵

[AS=SB=x

BT=TC=y

CU=UD=z

DV=VE=a

ER=RA=b]

adding downwards

2(x+y+z+a+b)=10+13+11+12+12=58

x+y+z+a+b=58/2=29

(x+y)+(z+a)+b=29

13+12+b=29

b=29-25=4

b=4

4+x=10

x=6

6+y=13

y=13-6=7

7+z=11

z=11-7=4

4+a=12

a=12-4=8

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x