To find the value of m3 when given that lines l and m are parallel, and we know that m5 is 38 degrees and m6 is 62 degrees, we can use the properties of parallel lines.
When two parallel lines are cut by a transversal, several angle relationships come into play. The key relationships to remember are:
- Corresponding angles
- Alternate interior angles
- Consecutive interior angles
- Alternate interior angles
In this case, we are interested in finding m3. Depending on its position relative to m5 and m6, we can apply the corresponding property. We can assume m3 is in a position where it relates to m5 as an alternate interior angle. Since m5 measures 38 degrees, we can conclude:
- If m3 is an alternate interior angle to m5, then m3 = m5 = 38 degrees.
On the other hand, if m3 is a consecutive interior angle to m6, we can calculate it as follows:
- m3 + m6 = 180 degrees
Substituting in the value of m6, we have:
- m3 + 62 = 180
Solving this equation:
- m3 = 180 – 62
- m3 = 118 degrees
Therefore, based on the relationships established, the value of m3 could either be 38 degrees if it corresponds to m5, or 118 degrees if it is supplementary to m6. Without loss of generality, you could use either value depending on the specific geometric configuration you’re working with.