Home » » TQ is tangent to circle XYTR, < YXT = 32$$^{\circ}$$, RTQ = 40$$^{\circ}$$. F...

# 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$$^{\circ}$$

### 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$$^{\circ}$$

## 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$$^{\circ}$$