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P Q R S is a cyclic quadrilateral such...

`P Q R S` is a cyclic quadrilateral such that `P R` is a diameter of the circle. If `/_Q P R=67^@ and /_S P R=72^@,` then `/_Q R S=`
(a)`41^@` (b) `23^@` (c) `67^@` (d) `18^@`

Text Solution

Verified by Experts

Angle in a semicircle is `90^@`
Thus `/_PQR=/_PSR=90^@`
`/_QPS=/_QPR+/_RPS=67^@+72^@=139^@`
Sum of all angles of quadrilateral must be `360^@`
Thus, `90^@+90^@+139^@+/_QRS=360^@`
`/_QRS=41^@`
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