PQRS is a cyclic quadrilateral. If ∠QPS = 75o, what is the size of ∠QRS?
Question 1 Report
PQRS is a cyclic quadrilateral. If ∠QPS = 75o, what is the size of ∠QRS?
Answer Details
Since PQRS is a cyclic quadrilateral, the opposite angles of the quadrilateral add up to 180 degrees. That is,
∠PQS + ∠QRS = 180° and ∠QPS + ∠RQS = 180°
We are given that ∠QPS = 75°, so we can use the above equation to find ∠RQS.
∠QPS + ∠RQS = 180°
75° + ∠RQS = 180°
∠RQS = 180° - 75° = 105°
Therefore, the size of ∠QRS is 105°. Option (C) "105" is the correct answer.
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