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The problem in the image involves finding the angle \( x \), given several angles in a diagram with wires and poles. Based on what I can observe, here’s how we can approach solving for \( x \):

1. The two given angles in the diagram are \( 35^\circ \) and \( 140^\circ \).
2. Since the wire and poles form a system of straight lines, we can use the fact that the sum of angles around a point on a straight line is always \( 180^\circ \).

Let's break down the problem step by step:

- The \( 140^\circ \) angle is given where the pole and the wire meet, which means that the angle on the other side of this straight line will be \( 180^\circ - 140^\circ = 40^\circ \).
- The \( 35^\circ \) angle is also given on the other side of the diagram.
- Now, we know that the total sum of angles around a point in a triangle must add up to \( 180^\circ \).

Using the known angles, we can now find \( x \).

1. The sum of the angles in the triangle (including \( 35^\circ \), \( 40^\circ \), and \( x \)) must equal \( 180^\circ \).
   
\[
35^\circ + 40^\circ + x = 180^\circ
\]

2. Solving for \( x \):

\[
x = 180^\circ - 35^\circ - 40^\circ
\]
\[
x = 105^\circ
\]

Thus, the value of \( x \) is \( 105^\circ \).

Would you like further details or clarification? Here are some related questions for practice:

1. How would you solve for \( x \) if the angles were different?
2. What is the sum of interior angles of a triangle, and why is this important?
3. How would you use this method to solve for unknown angles in different polygons?
4. Can you calculate the complementary and supplementary angles of \( x \)?
5. What role does symmetry play in solving geometry problems involving angles?

**Tip:** Always remember that the sum of angles in a triangle is \( 180^\circ \), and this is crucial in many geometry problems.

Find the value of angle x in the diagram involving a pole and wires, given the angles 35° and 140°.

Explore how to solve for unknown angles in geometric figures using fundamental angle theorems. This problem demonstrates calculating the unknown angle in a triangular setup involving a pole and wires, using angles sum property and straight line theorem. Suitable for students in Grades 7 to 10.

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