To solve the problem from the image, let's go step by step. The problem involves a triangle $\triangle ABC$ where angles $\angle A$, $\angle B$, and $\angle C$ need to be determined. Some angles and measurements are provided in the problem:

• $m\angle 1 = 80^\circ$
• $m\angle 2 = 60^\circ$

Step 1: Understand the Given Information

Looking at the diagram:

1. The angles $m\angle 1$ and $m\angle 2$ are labeled inside the triangle.
2. The diagram shows the triangle $ABC$ with various interior angles.

Step 2: Calculate Missing Angles

To find the other angles within the triangle, we can use the following properties of triangles:

• The sum of interior angles of any triangle is $180^\circ$.

Using this property, we can calculate the missing angles.

Given:

• $m\angle A = m\angle 1 + m\angle 4$
• $m\angle B = m\angle 2 + m\angle 3$
• $m\angle C = m\angle 5$

Now we use the information provided:

• $m\angle 1 = 80^\circ$
• $m\angle 2 = 60^\circ$

The other angles $\angle 3$, $\angle 4$, and $\angle 5$ are missing.

Step 3: Solve for $m\angle 3$, $m\angle 4$, and $m\angle 5$

1. Calculate $m\angle 3$: Since $m\angle B = m\angle 2 + m\angle 3$, and the exterior angle $m\angle 3$ should sum with $m\angle 2$ to the total angle at point B.

2. Calculate $m\angle 4$: $m\angle 4$ can be found using similar reasoning.

3. Calculate $m\angle 5$: Since it's the remaining angle in the triangle, we use the fact that $m\angle A + m\angle B + m\angle C = 180^\circ$.

Since the diagram doesn't provide explicit numbers for these smaller angles, the next step is solving them using the relationships between these angles as defined by the geometric properties and the external angle theorem.

Final Step:

You can apply the geometric rules, especially:

$m\angle A + m\angle B + m\angle C = 180^\circ$ $m\angle 4 = 180^\circ - (m\angle 2 + m\angle 5)$ $m\angle 5 = 180^\circ - m\angle 1$

Using these equations, solve the individual angles in each small triangle.

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