PQRS is a cyclic quadrilateral. If ∠QPS = 75o, what is the size of ∠QRS?

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.