https://file.aiquickdraw.com/mathbot/file/1728660465723stju10zz.jpg

find the mesures of the angles one to five

Let's analyze the image and find the measures of the unknown angles labeled 1 through 5.

1. **Angle 1**:
   - We observe a right angle near angle 1, where a vertical and horizontal line meet. The total angle around this point is 90°. The other angle adjacent to angle 1 is given as 50°. Thus, we can calculate angle 1 by subtracting:
     \[
     \text{Angle 1} = 90° - 50° = 40°.
     \]

2. **Angle 2**:
   - Angle 2 lies on a straight line with angle 1. The sum of angles on a straight line is 180°. Therefore, angle 2 can be found by subtracting angle 1 from 180°:
     \[
     \text{Angle 2} = 180° - 40° = 140°.
     \]

3. **Angle 3**:
   - Angle 3 is vertically opposite to the given angle of 55°. Vertically opposite angles are always equal. Therefore, we have:
     \[
     \text{Angle 3} = 55°.
     \]

4. **Angle 4**:
   - Angle 4 lies on a straight line with angle 3. The sum of angles on a straight line is 180°. So, we can find angle 4 by subtracting angle 3 from 180°:
     \[
     \text{Angle 4} = 180° - 55° = 125°.
     \]

5. **Angle 5**:
   - Similar to angle 3, angle 5 is vertically opposite to angle 4. Therefore, angle 5 is also equal to angle 4:
     \[
     \text{Angle 5} = 125°.
     \]

### Summary of angle measures:
- Angle 1: 40°
- Angle 2: 140°
- Angle 3: 55°
- Angle 4: 125°
- Angle 5: 125°

Would you like more details or clarification on any part of the solution?

Here are five related questions you can explore:
1. What is the sum of interior angles in any triangle?
2. How do we know that vertically opposite angles are equal?
3. What is the exterior angle theorem, and can it apply here?
4. Can we solve for angles using trigonometric functions in this diagram?
5. How do we calculate the sum of angles around a point?

**Tip:** Always remember that angles on a straight line add up to 180°, and angles around a point sum to 360°.

In this problem, learn how to calculate the measures of angles 1 to 5 using properties of vertically opposite angles, angles on a straight line, and the sum of angles around a point. Includes step-by-step solutions with key geometric formulas and theorems. Suitable for Grades 7-9.

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