https://file.aiquickdraw.com/mathbot/file/1725940124719fm8nlcn6.jpg

To solve question 35, we need to find the measures of ∠ADB and ∠BDC formed between the escalators. From the image, we observe the following:

- Angle ∠ADB is given as \(6x + 10^\circ\)
- Angle ∠BDC is given as \(4x^\circ\)

Since ∠ADB and ∠BDC are opposite each other, they are supplementary, meaning their sum is \(180^\circ\) because they form a straight line. This gives the equation:

\[
(6x + 10^\circ) + 4x^\circ = 180^\circ
\]

Let's solve this equation for \(x\).

\[
6x + 10 + 4x = 180
\]

\[
10x + 10 = 180
\]

\[
10x = 180 - 10
\]

\[
10x = 170
\]

\[
x = \frac{170}{10} = 17
\]

Now that we have \(x = 17\), we can substitute this value back into the expressions for ∠ADB and ∠BDC to find the measures of both angles.

\[
\text{∠ADB} = 6x + 10 = 6(17) + 10 = 102 + 10 = 112^\circ
\]

\[
\text{∠BDC} = 4x = 4(17) = 68^\circ
\]

Thus, the measures of the angles are:
- ∠ADB = \(112^\circ\)
- ∠BDC = \(68^\circ\)

Let me know if you want further details or if you have any questions!

---

Here are 5 related questions:
1. What are vertical angles and how do they relate to the problem?
2. Can you explain how supplementary angles work in more detail?
3. How would the solution change if the escalators created a different angle pair, say \(5x + 20^\circ\) and \(3x^\circ\)?
4. How do we know that ∠ADB and ∠BDC are on a straight line?
5. What would the sum of the angles be if the lines were not straight but formed a different shape?

**Tip:** Always look for relationships like supplementary or complementary angles when solving angle problems involving straight lines.

Find the measures of ∠ADB and ∠BDC formed between the escalators shown at the right.

Learn how to solve the problem of finding the measures of ∠ADB and ∠BDC between escalators using the concept of supplementary angles. This detailed solution involves algebraic manipulation and understanding of linear pairs. Ideal for students in 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