https://file.aiquickdraw.com/mathbot/file/1727351004498bjpkhvhq.jpg

The diagram shows two triangles and one additional angle, and we are tasked with finding the measures of the numbered angles (1 through 5).

### Step-by-step solution:

#### 1. Analyze the triangle with angles 50°, 65°, and angle 1:
- The sum of the angles in a triangle is always 180°. 
- Therefore, for the first triangle:
\[
50^\circ + 65^\circ + \text{angle 1} = 180^\circ
\]
\[
\text{angle 1} = 180^\circ - (50^\circ + 65^\circ) = 180^\circ - 115^\circ = 65^\circ
\]
So, **angle 1 = 65°**.

#### 2. Analyze angle 2:
- Angle 2 and angle 1 are **vertically opposite angles**, and vertically opposite angles are always equal.
- Therefore, **angle 2 = 65°**.

#### 3. Analyze angle 3:
- Angles 2 and 3 form a **linear pair**, which means they sum up to 180°.
\[
\text{angle 2} + \text{angle 3} = 180^\circ
\]
\[
65^\circ + \text{angle 3} = 180^\circ
\]
\[
\text{angle 3} = 180^\circ - 65^\circ = 115^\circ
\]
So, **angle 3 = 115°**.

#### 4. Analyze angle 4:
- Angle 4 is vertically opposite to angle 3, and as mentioned before, vertically opposite angles are equal.
- Therefore, **angle 4 = 115°**.

#### 5. Analyze angle 5:
- We are given the exterior angle of 140°, and this is equal to the sum of the two interior opposite angles (angles 4 and 5) in the lower triangle.
- Using the exterior angle theorem:
\[
\text{angle 4} + \text{angle 5} = 140^\circ
\]
\[
115^\circ + \text{angle 5} = 140^\circ
\]
\[
\text{angle 5} = 140^\circ - 115^\circ = 25^\circ
\]
So, **angle 5 = 25°**.

### Final Answers:
- **Angle 1 = 65°**
- **Angle 2 = 65°**
- **Angle 3 = 115°**
- **Angle 4 = 115°**
- **Angle 5 = 25°**

---

Do you want more details on any step or have any questions?

Here are 5 related questions you could explore:
1. How do you prove the exterior angle theorem?
2. What are the properties of vertically opposite angles?
3. How do linear pairs of angles relate to parallel lines?
4. Can angles be congruent even if they don't share a common vertex?
5. What is the sum of angles in polygons other than triangles?

**Tip**: When dealing with triangles, always remember that the sum of interior angles is 180°, and exterior angles provide a shortcut to find unknown interior angles!

Find the measure of each numbered angle in the provided geometric figure consisting of two triangles and additional angles.

Learn how to find the numbered angles in a geometric figure consisting of triangles and additional angles. Explore key concepts like the triangle angle sum theorem, vertically opposite angles, and exterior angle theorem. Suitable for students in Grades 7-9.

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