In this triangle-based problem, you're given a diagram with six angles labeled $m\angle 1$, $m\angle 2$, $m\angle 3$, $m\angle 4$, $m\angle 5$, and $m\angle 6$, along with angle measures: 50°, 60°, 70°, 110°, and 130°. The goal is to match each angle to the correct measure based on the following information:

• $m\angle 1 = 130^\circ$
• $m\angle 7 = 70^\circ$

Let’s break this down using the diagram and match the angles to the corresponding measures.

Step-by-Step Explanation:

1. Look at the angles in the triangle: The angles inside the triangle must add up to 180°, as per the triangle angle sum theorem.

2. Use the given angles:

   • Since $m\angle 1 = 130^\circ$, it’s an external angle. By the exterior angle theorem, $m\angle 1$ is the sum of the two non-adjacent interior angles, so $m\angle 2 + m\angle 3 = 130^\circ$.
   • $m\angle 7 = 70^\circ$ is also given, and it should match one of the interior angles.

3. Apply the measures:

   • The larger external angles are likely to be $m\angle 1$ (130°) and $m\angle 5$ (110°).
   • Smaller interior angles will correspond to measures like 50°, 60°, and 70°.

4. Start matching:

   • Based on the triangle’s external and internal configuration, let’s begin matching.

From this, we can fill out the table:

• $m\angle 1 = 130^\circ$
• $m\angle 2 = 50^\circ$
• $m\angle 3 = 60^\circ$
• $m\angle 4 = 70^\circ$
• $m\angle 5 = 110^\circ$
• $m\angle 6 = 120^\circ$

If you need more clarification or details, feel free to ask!

5 Relative Questions:

1. What is the exterior angle theorem, and how does it apply here?
2. Why do the internal angles of a triangle add up to 180°?
3. Can you provide more examples of matching angles with measures using the exterior angle theorem?
4. How do you differentiate between external and internal angles in complex shapes?
5. How would the problem change if the given angle measures were different?

Tip:

Always double-check your total sum when dealing with triangle angle problems—internal angles should always sum to 180°.