https://file.aiquickdraw.com/mathbot/file/1725637481439k743byv0.jpg

In this image, we have a set of intersecting lines where:

- One angle is labeled as \(87^\circ\).
- Two angles are labeled \(a^\circ\) and \(b^\circ\).
- It is mentioned that \(b\) is 2 times larger than \(a\), so we can express this as \(b = 2a\).

### Step-by-step Solution:

1. **Using the straight angle property:**
   The angles on a straight line sum to \(180^\circ\). So, the angle adjacent to the \(87^\circ\) is:
   \[
   180^\circ - 87^\circ = 93^\circ.
   \]

2. **Using angle relationships:**
   Since the angles \(a^\circ\) and \(b^\circ\) are part of a linear pair with the angle \(93^\circ\), we know that:
   \[
   a + b = 93^\circ.
   \]

3. **Substitute \(b = 2a\) into the equation:**
   \[
   a + 2a = 93^\circ,
   \]
   \[
   3a = 93^\circ,
   \]
   \[
   a = \frac{93^\circ}{3} = 31^\circ.
   \]

4. **Find \(b\):**
   Since \(b = 2a\):
   \[
   b = 2 \times 31^\circ = 62^\circ.
   \]

### Final Values:
- \(a = 31^\circ\)
- \(b = 62^\circ\)

Would you like more details or clarifications on this solution? 

Here are 5 related questions to further explore this topic:
1. How do complementary and supplementary angles differ?
2. What is the importance of vertical angles in geometry?
3. Can you explain the concept of adjacent angles?
4. What other relationships exist between intersecting lines?
5. How would the solution change if \(b = 3a\) instead of \(2a\)?

**Tip:** Always look for relationships such as straight lines and angle pairs (like vertical or adjacent angles) to simplify solving geometric problems.

In the image, we are given a set of intersecting lines where angle 'b' is 2 times larger than angle 'a', and one of the angles is 87°. We are tasked with finding the values of 'a' and 'b'.

This problem involves solving for angles 'a' and 'b' where 'b' is twice the size of 'a', and a third angle is given as 87°. By using linear pair relationships and basic algebraic equations, the values of 'a' and 'b' are determined. Suitable for students in Grades 7-9.

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