Multiple Choice
Which of the following angles in standard position is an acute angle?
1. Measuring Angles
Angles in Standard Position
Multiple Choice
If and are two angles in standard position, which angle has a measure equal to the sum of and ?
A
is equal to
B
C
D
Verified step by step guidance1
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 \( Q \).
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 \( S \).
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 \( Q \)).
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.
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.
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