https://file.aiquickdraw.com/mathbot/file/1730230714687nnwtz754.jpg

Find the value of *x* in the given figure using properties of parallel lines.

Question 10 options:

A)

105°

B)

75°

C)

35°

D)

15°

To find the value of \( x \) in this figure, we can use properties of parallel lines and the concept of vertically opposite angles and alternate interior angles.

### Solution Steps:

1. **Identify Parallel Lines and Transversals**:
   In the figure, lines \( l \) and \( m \) appear to be parallel, with line \( n \) acting as a transversal intersecting both \( l \) and \( m \).

2. **Identify Given Angles**:
   The angle given is \( 105^\circ \), which is an exterior angle created by the transversal \( n \) and parallel lines \( l \) and \( m \).

3. **Apply the Alternate Interior Angles Property**:
   Since \( l \) and \( m \) are parallel, the angle on the opposite side of the transversal (the angle labeled \( x \)) is an alternate interior angle to the \( 105^\circ \) angle.

   According to the alternate interior angle theorem, alternate interior angles are equal when two parallel lines are intersected by a transversal.

4. **Conclude the Value of \( x \)**:
   Since angle \( x \) is an alternate interior angle to the \( 105^\circ \) angle, we have:
   \[
   x = 105^\circ
   \]

### Answer:
The value of \( x \) is \( \boxed{105^\circ} \).

Would you like further details, or do you have additional questions?

---

Here are five related questions to expand your understanding:

1. What are alternate interior angles, and how are they used in parallel line problems?
2. What are some other types of angle pairs formed when two parallel lines are intersected by a transversal?
3. How can we determine if two lines are parallel based on given angles?
4. What are vertically opposite angles, and how do they relate to each other?
5. How do we determine angles when we are only given supplementary angles?

**Tip:** Remember that alternate interior angles are always equal when lines are parallel, a useful property for solving many geometric problems involving parallel lines.

Find the value of x in the given figure using properties of parallel lines.

Learn how to find the value of angle x in a geometric figure with parallel lines. This problem uses the Alternate Interior Angle Theorem and is ideal for students in Grades 7-9, covering essential geometry concepts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation