For the proof given above, what is missing in Statement #8

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Use this figure.
Figure 5: RT is a tangent segment, m Ang T = 50, and m Arc RX = 100.

Proof:
Statement 1: m Arc RX = 100. Reason 1: Given
Statement 2: m Ang RSX = ______. Reason 2: The measure of an inscribed angle is ½ the measure of the intercepted arc.
Statement 3: m Ang RSX = 50. Reason 3: Substitution
Statement 4: m Ang T = 50. Reason 4: Given
Statement 5: m Ang T = m Ang RSX. Reason 5: Substitution
Statement 6: Ang T = Ang RSX. Reason 6: Definition of congruent angles
Statement 7: RT is a tangent segment. Reason 7: Given
Statement 8: m Ang TRS = _____. Reason 8:An angle formed by a secant and a tangent is ___ the measure of its intercepted arc.
Statement 9: m Ang SXR = ½ m Arc RS. Reason 9:The measure of an inscribed angle is ½ the measure of the intercepted arc.
Statement 10: m Ang TRS = m Ang SXR. Reason 10: Substitution
Statement 11: Ang TRS = Ang SXR. Reason 11: Definition of congruent angles
Statement 12: Triangle RST is similar to Triangle XRS. Reason 12: ___ Similarity Theorem




Question 20
20: For the proof given above, what is missing in Statement #8?
Question 21
21: For the proof given above, what is missing in Reason #8?
Question 22
22: For the proof given above, what is missing in Reason #12?

My Answers Are:

20. ½ m Arc RX?
21. SSS?
22. AA

20. Statement 8: ½ m Arc RS

21. Reason 8: half

22. Statement 12: AA (2 congruent angles ---> 3 congruent angles ---> similar triangles)

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