वृत्त के बिंदु P पर स्पर्श रेखा ST तथा QR वृत्त का व्यास है। यदि `angleRPT=50^(@)` है, तब `angleSPQ` है।

Options

A. `40^(@)`
B. `60^(@)`
C. `80^(@)`
D. `100^(@)`

Answer

A

Explanation

According to question,

`angleRPT= 50^(@)`
`angleQPR = 90^(@)` (Angle in semicircle)
`therefore anglePOR=50^(@)`
alternate segment theorem
In `DeltaPQR`
`angleP+angleQ+angleR=180^(@)`
`angleR = 180^(@)-90^(@)-50^(@)`
`angleR = 40^(@)`
`therefore angleSPQ = 40^(@)` (Alternate segment theorem)