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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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Dicussion (1)

  • < 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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