Answered

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In ΔQRS, given m∠Q = 80°, m∠R = 65°, and m∠S = 35°, which side of ΔQRS is the longest?

A. RS
B. QS
C. QR
D. Cannot be determined

Sagot :

GinnyAnsweridn
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
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