Adjacent Angles Problem: Finding Pairs That Sum to 180 Degrees

Question

The sum of the adjacent angles is 180

Step-by-Step Solution

To determine if the statement that "the sum of the adjacent angles is 180" is true, follow these steps:

  • Step 1: Define Adjacent Angles

    Adjacent angles are two angles that have a common vertex and a common side but do not overlap. In geometry, when these angles form a straight line, they are known as a linear pair.

  • Step 2: Apply the Linear Pair Theorem

    The Linear Pair Theorem states that if two angles are adjacent and form a linear pair (i.e., the non-common sides form a straight line), then these angles are supplementary. This means that their sum is 180180^\circ.

  • Step 3: Conclusion

    Therefore, when adjacent angles form a linear pair on a straight line, their sum is indeed 180180^\circ.

This validates the statement that "the sum of the adjacent angles is 180" for linear pairs, making the statement True.

This corresponds to the answer choice stating: True.

Answer

True