Which equation can be used to solve for
\[x\] in the following diagram?
Two lines intersect forming angles. One of the angles is marked and labeled as 110 degrees. Another angle opposite to this is marked and labeled as parenthesis open 10 times x plus 10 parenthesis closed degrees. The angle between these two is divided by a ray into two parts.
\[110^\circ\]
\[{(10x + 10)^\circ}\]
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[(10x + 10) =110\]
A
\[(10x + 10) =110\]
(Choice B)
\[(10x + 10) - 110 = 90\]
B
\[(10x + 10) - 110 = 90\]
(Choice C)
\[(10x + 10) + 110 = 180\]
C
\[(10x + 10) + 110 = 180\]
(Choice D)
\[(10x + 10) = 90\]
D
\[(10x + 10) = 90\]

To solve this problem, let's consider the properties of angles formed when two lines intersect.

When two lines intersect, they form two pairs of opposite (or vertical) angles. These vertical angles are always equal. 

Given in the diagram:
- One angle is \(110^\circ\).
- The opposite angle is labeled as \((10x + 10)^\circ\).

Since these are vertical angles, they must be equal. Therefore, we can set up the equation:

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

This matches **Choice A**.

**Correct Answer:**
- **(Choice A) \((10x + 10) = 110\)**

Would you like further details or have any questions?

---

Here are 5 related questions:
1. What are vertical angles and why are they always equal?
2. How do you solve the equation \((10x + 10) = 110\) for \(x\)?
3. What other properties of angles are formed when two lines intersect?
4. How can you verify the solution for \(x\) once it’s found?
5. What are supplementary angles and how are they different from vertical angles?

**Tip:** Remember that when two lines intersect, vertical angles are always equal. This property can help solve many geometric problems involving angles.

Learn how to solve angle problems involving vertical angles formed by intersecting lines. This problem specifically addresses finding the value of x using the vertical angles theorem. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation