Question

Pentagon RSTUV is circumscribed about a circle. What is the value of x if RS = 6, ST = 9, TU = 7, UV = 15, and VR = 14?

Answer 1

Starting at vertex V going until vertex S, we make our calculations.

VR = 14

Rx = x

therefore, xS = VR – Rx

xS = 14 – x ---> 1

Now starting at vertex V going left to vertex S, we make our next set of calculations. Assuming x is on VR but nearer R

VR = 14 - x

at UV = 15 – (14 – x)

at UV = 1 + x

at TU = 7 – (1 + x)

at TU = 6 – x

at ST = 9 – (6 – x)

at ST = 3 + x ---> 2

Equate 1 and 2:

14 – x = 3 + x

2 x = 11

x = 5.5