Triangle Q R S is shown with exterior angles. Line R Q extends through point D. Line Q R extends through point E. Line Q S extends through point C. Which angle has a measure equal to the sum of m∠SQR and m∠QRS?∠RSC∠SRE∠DQS∠QSR

Answer:Option A.Step-by-step explanation:In triangle QRS, Line R Q extends through point D. Line Q R extends through point E. Line Q S extends through point C as shown below.We need to find an angle that has a measure equal to the sum of m∠SQR and m∠QRS.According to the exterior angle theorem, the measure of an exterior angle of a triangle is equal to the sum of measures of two opposite interior angles.Since ∠SQR and ∠QRS are two interior angles of a triangle QRS, so ∠RSC is the exterior angle of opposite to ∠SQR and ∠QRS.By using exterior angle theorem we conclude thatm∠RSC = m∠SQR + m∠QRS∠RSC has a measure equal to the sum of m∠SQR and m∠QRS.Therefore, the correct option is A.