If $m\angle \mathrm{SQR}$ and $m\angle \mathrm{QRS}$ are two angles in standard position, which angle has a measure equal to the sum of $m\angle \mathrm{SQR}$ and $m\angle \mathrm{QRS}$?

• A. $m\angle \mathrm{SQS}+m\angle \mathrm{QRS}$ is equal to $m\angle \mathrm{SQR}+m\angle \mathrm{QRS}$
• B. $m\angle \mathrm{SRS}$
• C. $m\angle \mathrm{SQS}+m\angle \mathrm{QRS}$
• D. $m\angle \mathrm{SQS}$

Answer: (A)

Verified step by step guidance

1. Identify the points and angles involved: We have angles \( m\angle SQR \) and \( m\angle QRS \), which share a common vertex \( Q \) and points \( S, R \), and \( Q \).
2. Recall that the measure of an angle formed by three points is the angle at the middle point. So, \( m\angle SQR \) is the angle at point \( Q \) formed by points \( S \) and \( R \), and \( m\angle QRS \) is the angle at point \( R \) formed by points \( Q \) and \( S \).
3. To find an angle whose measure equals the sum \( m\angle SQR + m\angle QRS \), consider the angle \( m\angle SQS \), which is formed by points \( S, Q, S \) (note that this is a conceptual step to understand the sum of adjacent angles around point \( Q \)).
4. Use the Angle Addition Postulate: If two angles share a common side and vertex, the measure of the larger angle formed by the non-common sides is the sum of the two smaller angles. Here, \( m\angle SQS + m\angle QRS = m\angle SQR + m\angle QRS \) implies that \( m\angle SQS + m\angle QRS \) equals the sum of the original two angles.
5. Therefore, the angle \( m\angle SQS + m\angle QRS \) represents the sum of \( m\angle SQR \) and \( m\angle QRS \). This shows which angle measure equals the sum of the two given angles.