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

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 that

m∠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.

Oh My Gosh!  

My best choice is A.