When two lines intersect, they form four angles at the point of intersection. The properties of linear pairs and vertical angles help determine these angles as follows:
- Linear pairs are pairs of adjacent angles formed by the intersecting lines that share a common side and vertex. The key property is that linear pairs are supplementary, meaning their measures add up to 180 degrees. So, if you know the measure of one angle, you can find its linear pair by subtracting from 180 degrees.
- Vertical angles (also called vertically opposite angles) are pairs of angles opposite each other at the intersection point. These angles are congruent, meaning they have equal measures.
Using these properties together:
- If you know the measure of one angle formed by the intersecting lines, you can find its adjacent angle (linear pair) by subtracting from 180 degrees.
- Then, using the vertical angles property, you know the angle opposite the original angle is equal to it.
- Similarly, the angle opposite the adjacent angle is equal to the adjacent angle.
Thus, knowing one angle measure allows you to determine all four angles created by the intersecting lines. In summary, linear pairs tell you adjacent angles sum to 180°, and vertical angles tell you opposite angles are equal. These relationships fully determine the angle measures formed by two intersecting lines
