Question

which sign explains the relationship between m∠1 and m∠2 in the diagram? (diagram of two triangles with side lengths 17 m and 23 m, and marked angles ∠1 and ∠2)

Explanation:

Step1: Identify Triangle Properties

In a triangle, the larger side is opposite the larger angle, and the smaller side is opposite the smaller angle. Both triangles have two sides with the same markings (indicating congruent sides), so they are isosceles triangles.

Step2: Compare Opposite Sides

For ∠1, the opposite side is 17 m. For ∠2, the opposite side is 23 m. Since 17 < 23, the angle opposite the smaller side (∠1) is smaller than the angle opposite the larger side (∠2). So \( m\angle1 < m\angle2 \), and the sign is \( < \).

Answer:

\( < \) (less than sign)