Question

m∠1=
m∠2=
m∠3=
m∠4=
m∠5=

1. put the angles of this triangle in order from smallest to largest

Explanation:

Step1: Recall Triangle Angle-Side Relationship

In a triangle, the larger the side length, the larger the opposite angle. So we first identify the side lengths and their opposite angles.

• Side opposite \( \angle 1 \): length \( 15 \)
• Side opposite \( \angle 2 \): length \( 16 \)
• Side opposite \( \angle 3 \): length \( 17 \)

Step2: Compare Side Lengths

Compare the side lengths: \( 15 < 16 < 17 \).

Step3: Relate to Angles

Since the side opposite \( \angle 1 \) (15) is the shortest, \( \angle 1 \) is the smallest. The side opposite \( \angle 2 \) (16) is middle - length, so \( \angle 2 \) is middle - sized. The side opposite \( \angle 3 \) (17) is the longest, so \( \angle 3 \) is the largest.

Answer:

\( \angle 1 < \angle 2 < \angle 3 \)