Answer :
Final answer:
The measure of angle QPS is 70°. None of the above option.
Explanation:
To find the measure of angle QPS, we can use the property that the angles formed by a chord subtended at the circumference of a circle are equal. In this case, RSQ is equal to RQS because they both subtend the same arc. Since RSQ = 110°, this means that RQS = 110° as well. Because RSQ is a straight line, therefore ∠QRS + ∠QRO = 180°.
But it is known that RSQ = 110° which is an angle at the center. Hence, ∠QRS = 180° − 110° = 70°. In a cyclic quadrilateral, the sum of opposite angles is 180°. Therefore, ∠QPS + ∠QRO = 180°. As ∠QRO = 110°, then ∠QPS = 180° − 110° = 70°. Since RQS and QPS form a straight line, their sum is 180°. So, QPS = 180° - RQS = 180° - 110° = 70°. None of the above option.
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