https://file.aiquickdraw.com/mathbot/file/17265907457099yb4y0sm.jpg

The given image shows a geometric figure with multiple angles, and we are asked to find the value of the angle marked as "?" in the diagram.

### Here's how we can solve it step-by-step:

1. **Identify the key angles in the figure**:
   - There is an angle labeled as 126°.
   - There is an angle labeled as 55° adjacent to the unknown angle "?".
   - There is a straight line with angles of 142° and 101° on either side of the line.

2. **Use the fact that angles on a straight line sum to 180°**:
   - The angle next to the 142° is the exterior angle, marked as 126°. Therefore, the angle adjacent to 126° on the straight line is:
   \[
   180^\circ - 126^\circ = 54^\circ
   \]
   This is the angle next to the 126°.

3. **Use the triangle angle sum theorem**:
   - In the triangle with angles 55°, "?" (the unknown angle), and 54° (calculated in step 2), the sum of the angles in a triangle must always equal 180°.
   
   Therefore, we can set up the equation:
   \[
   55^\circ + 54^\circ + ? = 180^\circ
   \]

4. **Solve for the unknown angle**:
   \[
   ? = 180^\circ - 55^\circ - 54^\circ = 71^\circ
   \]

Thus, the value of the unknown angle "?" is **71°**.

Would you like a detailed explanation on any step or further clarifications?

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Here are 5 related questions for practice:
1. How do you calculate the exterior angle of a triangle?
2. What is the relationship between angles on a straight line?
3. How do you apply the angle sum property of a triangle in more complex polygons?
4. How can you use vertical and supplementary angles to solve for unknown angles?
5. What are alternate interior angles, and how do they help in solving angle problems?

**Tip:** When solving for unknown angles in a figure, always look for straight lines, triangles, or parallel lines to use angle properties effectively!

Calculate the measure of the angle marked ? in the given image.

Learn how to calculate the unknown angle in a geometric figure using the Triangle Angle Sum Theorem and supplementary angles on a straight line. This step-by-step solution is suitable for students in Grades 7-10, helping to understand core geometry concepts.

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