To determine which side of triangle AQRS is the longest, we can use the properties of triangles, specifically the relationship between the angles and the sides opposite them.
### Step-by-Step Solution:
1. Understand the Given Angles:
- [tex]\( \angle Q = 80^\circ \)[/tex]
- [tex]\( \angle R = 65^\circ \)[/tex]
- [tex]\( \angle S = 35^\circ \)[/tex]
2. Recall the Triangle Angle-Side Relationship:
In any triangle, the side opposite the largest angle is the longest. Similarly, the side opposite the smallest angle is the shortest.
3. Identify the Largest Angle:
- The given angles are [tex]\( 80^\circ \)[/tex], [tex]\( 65^\circ \)[/tex], and [tex]\( 35^\circ \)[/tex]. Among these, [tex]\( 80^\circ \)[/tex] is the largest angle.
4. Determine the Longest Side:
- The side opposite [tex]\( \angle Q \)[/tex] (which is [tex]\( 80^\circ \)[/tex]) will be the longest.
5. Identify the Corresponding Side:
- The side opposite [tex]\( \angle Q \)[/tex] must be RS because it completes the triangle with the other two angles.
Thus, the side RS is the longest in triangle AQRS.
Answer:
A. RS
