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 exten
ds through point C.
Which angle has a measure equal to the sum of m∠SQR and m∠QRS?
∠RSC
∠SRE
∠DQS
∠QSR
Which angle has a measure equal to the sum of m∠SQR and m∠QRS?
∠RSC
∠SRE
∠DQS
∠QSR
2 answers:
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 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.
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