TQ is tangent to circle XYTR, < YXT = 32\(^{\circ}\), RTQ = 40\(^{\circ}\). F...
Question
TQ is tangent to circle XYTR, < YXT = 32\(^{\circ}\), RTQ = 40\(^{\circ}\). Find < YTR
Options
A) 108\(^{\circ}\)
B) 121\(^{\circ}\)
C) 140\(^{\circ}\)
D) 148\(^{\circ}\)
The correct answer is A.
Explanation:
< TWR = < QTR = 40\(^{\circ}\) (alternate segment)
< TWR = < TXR = 40\(^{\circ}\)(Angles in the same segments)
< YXR = 40\(^{\circ}\) + 32\(^{\circ}\) = 72\(^{\circ}\)
< YXR + < YTR = 180\(^{\circ}\)(Supplementary)
72\(^{\circ}\) + < YTR = 180\(^{\circ}\)
< YTR = 180\(^{\circ}\) - 72\(^{\circ}\)
= 108\(^{\circ}\)
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< TWR = < QTR = 40\(^{\circ}\) (alternate segment)
< TWR = < TXR = 40\(^{\circ}\)(Angles in the same segments)
< YXR = 40\(^{\circ}\) + 32\(^{\circ}\) = 72\(^{\circ}\)
< YXR + < YTR = 180\(^{\circ}\)(Supplementary)
72\(^{\circ}\) + < YTR = 180\(^{\circ}\)
< YTR = 180\(^{\circ}\) - 72\(^{\circ}\)
= 108\(^{\circ}\)