In the diagram above, PQRS s a cyclic quadrilateral, ?PSR = 86o and ?QPR = 38o. Calculate PRQ

In the diagram above, PQRS s a cyclic quadrilateral, ?PSR = 86^o and ?QPR = 38^o. Calculate PRQ

Answer Details

In a cyclic quadrilateral, the opposite angles add up to 180 degrees. Therefore, we can find the value of angle PQR as follows: angle PSR + angle PQR = 180 (since PQRS is a cyclic quadrilateral) 86 + angle PQR = 180 angle PQR = 180 - 86 = 94 degrees We are given angle QPR as 38 degrees, and since angles in a triangle add up to 180 degrees, we can find angle PRQ as: angle PRQ = 180 - angle PQR - angle QPR angle PRQ = 180 - 94 - 38 angle PRQ = 48 degrees Therefore, the answer is option (C) 48^o.