In this image, the task is to identify the largest and smallest angles in each triangle and then arrange the angles in both increasing and decreasing order.

To help with the identification, we need to use the property of triangles that relates side lengths and angles. The largest angle in a triangle is opposite the longest side, and the smallest angle is opposite the shortest side.

Let's break it down step by step for each triangle:

1. Triangle ABC:

• Sides: AB = 7, BC = 9, AC = 5

• The longest side is BC (9), so the largest angle is opposite this side (angle A).

• The shortest side is AC (5), so the smallest angle is opposite this side (angle B).

  Largest Angle: A Smallest Angle: B

  Increasing Order: B, C, A
  Decreasing Order: A, C, B

2. Triangle DEF:

• Sides: DE = 8, EF = 6, DF = 7

• The longest side is DE (8), so the largest angle is opposite this side (angle F).

• The shortest side is DF (7), so the smallest angle is opposite this side (angle E).

  Largest Angle: F
  Smallest Angle: E

  Increasing Order: E, D, F
  Decreasing Order: F, D, E

3. Triangle JKL:

• Sides: JK = 15, KL = 11, JL = 13

• The longest side is JK (15), so the largest angle is opposite this side (angle L).

• The shortest side is KL (11), so the smallest angle is opposite this side (angle J).

  Largest Angle: L
  Smallest Angle: J

  Increasing Order: J, K, L
  Decreasing Order: L, K, J

4. Triangle PQR:

• Sides: PQ = 6, QR = 7, PR = 4

• The longest side is QR (7), so the largest angle is opposite this side (angle P).

• The shortest side is PR (4), so the smallest angle is opposite this side (angle Q).

  Largest Angle: P
  Smallest Angle: Q

  Increasing Order: Q, R, P
  Decreasing Order: P, R, Q

5. Triangle STU:

• Sides: ST = 6, TU = 5, SU = 9

• The longest side is SU (9), so the largest angle is opposite this side (angle T).

• The shortest side is TU (5), so the smallest angle is opposite this side (angle S).

  Largest Angle: T
  Smallest Angle: S

  Increasing Order: S, U, T
  Decreasing Order: T, U, S

Would you like further details or clarifications on any of these steps?

Here are some related questions for you to explore:

1. What happens if two sides of a triangle are equal? How does this affect the angles?
2. Can you apply the same method to non-right triangles? Why or why not?
3. How do the exterior angles relate to the interior angles in a triangle?
4. How does the sum of the angles in a triangle relate to the largest and smallest angles?
5. What are the different types of triangles based on their angles and sides?

Tip: Remember that in any triangle, the sum of the angles is always 180°. This can be a useful check to verify your angle assignments.