Based on the calculations, the value of x in pentagon RSTUV is equal to 4.
How to determine the value of x?
Based on the diagram (see attachment), we can logically deduce the following points:
- The tangents drawn from a point out side the circle are the same (equal).
- Each side of pentagon RSTUV is a tangent to the circle.
Tangent RS = x + y
10 = x + y .....equation 1.
Tangent VR = x + n
12 = x + n .....equation 2.
Subtracting eqn. 2 from eqn. 1, we have:
y - n = -2 .....equation 3.
Tangent ST = y + z
13 = y + z .....equation 4.
Tangent TU = m + z
11 = m + z .....equation 5.
Subtracting eqn. 5 from eqn. 4, we have:
y - m = 2 .....equation 6.
Tangent UV = m + n
12 = m + n .....equation 7.
Adding eqn. 6 and eqn. 7, we have:
y + n = 14 .....equation 8.
Next, we would solve eqn. 3 and eqn. 8 simultaneously:
y - n = -2 .....equation 3.
y + n = 14 .....equation 8.
2y = 12
y = 6.
Now, we can solve for x from eqn. 1:
10 = x + y
10 = x + 6
x = 10 - 6
x = 4.
Read more on a circumscribed pentagon here: https://brainly.com/question/12925362
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