Question

question 30 of 50
which angle is the smallest?
x
52 52
y z
50
angle yzx
angle zyx
angle xyz
angle yxz
angle xzy

Explanation:

Step1: Recall Triangle Angle-Side Relationship

In a triangle, the smallest angle is opposite the shortest side. This is because of the angle - side relationship in triangles: larger sides are opposite larger angles and smaller sides are opposite smaller angles.

Step2: Identify Sides and Opposite Angles

• The side \( YZ = 50 \) is the shortest side among \( XY = 52 \), \( XZ = 52 \), and \( YZ=50 \).
• The angle opposite to side \( YZ \) is angle \( YXZ \) (angle at vertex \( X \), between sides \( XY \) and \( XZ \)).
• Now let's analyze the other angles:
• Angles \( ZYX \) (angle at \( Y \)) and \( YZX \) (angle at \( Z \)) are opposite the equal sides \( XZ = 52 \) and \( XY = 52 \) respectively. So angles \( ZYX \) and \( YZX \) are equal. Since \( YZ = 50\) is shorter than \( XY = 52\) and \( XZ = 52\), the angle opposite \( YZ \) (angle \( YXZ \)) should be smaller than angles \( ZYX \) and \( YZX \). Also, note that angle \( XYZ \) is the same as angle \( ZYX \) (just named differently) and angle \( XZY \) is the same as angle \( YZX \) (just named differently).

Answer:

angle YXZ