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To solve this, we analyze the geometric configuration given in the problem.

In the diagram, point \( E \) lies on line segment \( DF \). The angles around \( E \) are labeled \( a^\circ \) and \( b^\circ \), with two angles of \( b^\circ \) on either side of \( a^\circ \), making this an example of linear pair or supplementary angles.

Since angles on a straight line add up to \( 180^\circ \), we can form the following equation:
\[
a + 2b = 180
\]
Given that \( a \) and \( b \) are integers, we need to find possible integer values for \( a \).

Would you like me to solve this equation for \( a \) in terms of possible values of \( b \)? 

Here are five related questions:
1. How can we determine possible values for \( b \) that make \( a \) an integer?
2. If \( b = 60 \), what would the value of \( a \) be?
3. How does the concept of supplementary angles help in solving such problems?
4. Can there be multiple solutions for \( a \) and \( b \) if we add more constraints?
5. How does this problem change if we assume \( E \) is the midpoint of \( DF \)?

**Tip:** Remember that angles on a straight line always add up to \( 180^\circ \).

In the figure above, point E lies on DF and a and b are integers. Which could be a value of a?

Explore a geometry problem where angles around point E form a linear pair. Learn how to determine possible integer values for angle a, given that angles on a straight line add up to 180 degrees. Suitable for Grades 8-10.

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