https://file.aiquickdraw.com/mathbot/file/1726662508227q2c8kyo8.jpg

To solve for \( s \), we need to use the fact that the sum of the angles around the point where the lines intersect must add up to 180° (linear pair).

We are given three angles:
- \( (8s)^\circ \)
- \( (6s - 8)^\circ \)
- A right angle \( 90^\circ \)

These three angles form a straight line, so their sum must equal 180°.

Let's set up the equation:

\[
(8s) + (6s - 8) + 90 = 180
\]

Now, let's solve for \( s \). 

First, combine like terms:

\[
8s + 6s - 8 + 90 = 180
\]
\[
14s + 82 = 180
\]

Next, subtract 82 from both sides:

\[
14s = 180 - 82
\]
\[
14s = 98
\]

Now, divide both sides by 14:

\[
s = \frac{98}{14}
\]
\[
s = 7
\]

Thus, the value of \( s \) is \( 7 \).

Would you like a more detailed breakdown or have any questions?

Here are five related questions to deepen your understanding:
1. What are supplementary angles, and how do they apply to this problem?
2. How do you identify a linear pair of angles in a geometry problem?
3. What is the significance of a right angle in geometric equations like this?
4. If the angles were in a triangle instead of on a straight line, how would you approach the problem?
5. What happens if the angles given don't add up to 180° in such a scenario?

**Tip:** Always verify the sum of angles, especially when dealing with linear pairs or triangles, as these have fixed angle sums (180° for straight lines or triangles).

Solve for the value of s, given the angles (8s)°, (6s-8)°, and a right angle (90°) forming a linear pair.

Learn how to solve for the value of s by using the concept of supplementary angles and a linear pair. In this problem, the sum of angles including (8s)°, (6s-8)°, and 90° is set equal to 180°, and the solution involves algebraic manipulation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation