Question

Pentagon RSTUV is circumscribed about a circle. What is the value of x if RS=8, ST=12, TU=15, UV=9, and V=12?

Answer 1

Picture

Answer 2

\[x + y = 8\]\[y + z = 12\]\[z + a = 15\]\[a + b = 9\]\[b + x = 12\]
\[x - z = -4\]
\[x + a = 11\]
\[x - b = 2\]
\[x + x = 14\]\[2x = 14\]\[x = ?\]

Answer 3

I basically used the elimination method to continuously cancel the extra variables out. I also used the congruent tangents theorem.

Answer 4

Thank you. 2x=14 would turn into 7 correct?

Answer 5

Yes :)