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

In triangle QRS, the exterior angle theorem states that an exterior angle is equal to the sum of the two non-adjacent interior angles.

To find which angle has a measure equal to the sum of \( m∠SQR \) (which can also be referred to as angle QSR) and \( m∠QRS \) (which is angle RQS), we need to identify the applicable exterior angle.

Given the options:

1. \( ∠RSC \)
2. \( ∠SRE \)
3. \( ∠DQS \)
4. \( ∠QSR \)

The angle that is formed by extending line QR through point E is \( ∠SRE \). This angle is an exterior angle at vertex R of triangle QRS, equal to the sum of angles \( m∠SQR \) (which is \( ∠QSR \)) and \( m∠QRS \).

Thus, the angle that has a measure equal to the sum of \( m∠SQR \) and \( m∠QRS \) is:

**∠SRE**.