https://file.aiquickdraw.com/mathbot/file/17272834045082jadvqce.jpg

The image you've uploaded shows two pairs of vertical lines intersected by a transversal line. Specifically:

- Lines \( AB \parallel CD \) and \( EF \parallel GH \) are parallel to each other, and a transversal line cuts through all four lines.
- The angle at \( G \), labeled as \( (3x - 10)^\circ \), and the angle at \( H \), labeled \( 110^\circ \), form a pair of consecutive interior angles on the same side of the transversal.

### To solve for \( x \):

Since lines \( AB \parallel CD \) and \( EF \parallel GH \) are parallel, and the angles \( (3x - 10)^\circ \) and \( 110^\circ \) are consecutive interior angles (also known as co-interior or same-side interior angles), we know that their sum must equal 180°:

\[
(3x - 10)^\circ + 110^\circ = 180^\circ
\]

### Solve for \( x \):

\[
3x - 10 + 110 = 180
\]
\[
3x + 100 = 180
\]
\[
3x = 180 - 100
\]
\[
3x = 80
\]
\[
x = \frac{80}{3}
\]
\[
x \approx 26.67^\circ
\]

Thus, \( x \approx 26.67^\circ \).

Would you like more details or have any further questions?

---

Here are 5 related questions to expand your understanding:

1. What is the definition of co-interior (consecutive interior) angles?
2. How do we know when lines are parallel based on angle relationships?
3. Can corresponding angles be used to check if lines are parallel?
4. What other angle relationships exist when a transversal crosses parallel lines?
5. How would the calculation change if the given angle at \( H \) were different?

**Tip:** Always look for angle relationships such as corresponding, alternate interior, or co-interior angles when dealing with transversals and parallel lines.

Solve for x given that two parallel lines are intersected by a transversal. The angles at G and H are (3x - 10)° and 110°, respectively. Use consecutive interior angles to find the value of x.

Learn how to solve for x in a geometry problem involving parallel lines intersected by a transversal, where consecutive interior angles are given as (3x - 10)° and 110°. The solution involves the co-interior angles theorem and algebraic manipulation. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation