https://r2.erweima.ai/mathbot/image/1726042952995xknejqpy.jpg

The image shows a geometric problem where two lines \( l_1 \) and \( l_2 \) are parallel, and you need to calculate the angle \( x \) based on the given information. Here's a breakdown:

- There is a triangle with one vertex at the top and two angles on the base.
- The angle at the top vertex is \( 40^\circ \).
- There are two parallel lines \( l_1 \) and \( l_2 \) with an angle \( 70^\circ \) at the intersection point with \( l_1 \).

### Approach:

Since \( l_1 \parallel l_2 \), the angle \( 70^\circ \) and the angle next to \( x \) (which is labeled \( 40^\circ \)) are alternate interior angles. Alternate interior angles formed by a transversal line cutting through two parallel lines are equal.

To solve for \( x \):
1. The sum of the angles in a triangle is always \( 180^\circ \).
2. Using the angles in the triangle:
   \[
   x + 40^\circ + 70^\circ = 180^\circ
   \]
3. Solving this equation:
   \[
   x + 110^\circ = 180^\circ
   \]
   \[
   x = 180^\circ - 110^\circ
   \]
   \[
   x = 70^\circ
   \]

Thus, \( x = 70^\circ \).

Would you like further details or have any questions?

### 5 Related Questions:
1. What are alternate interior angles, and how are they used in geometry?
2. How does the property of parallel lines influence the angles in a transversal?
3. Can this method be applied to non-triangular figures with parallel lines?
4. What is the sum of interior angles in a polygon, and how does it change with the number of sides?
5. How do we apply the angle sum property in irregular triangles?

### Tip:
When working with triangles, always remember that the sum of all interior angles is \( 180^\circ \), and this rule can guide you in finding unknown angles.

Calculate the angle x if l1 is parallel to l2. Given angles: 40° at the vertex of the triangle, and 70° at the intersection of l1.

Solve for angle x in a geometric problem involving two parallel lines and a triangle. This solution uses the alternate interior angles theorem and the angle sum property of a triangle. Suitable for Grades 7-9.

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