Question

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 1

A

Explanation:

edge 2020 geometry quiz on triangle angle theorems

Answer 2

Option A.

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.