Question

question 15
a student claims the following
\if two angles are supplementary, then they must be adjacent angles.\
select all the counter - examples of the students claim
□ a linear pair of angles
□ a pair of vertical angles
□ a pair non - vertical angles formed by two intersecting lines.
□ two right angles that share a common vertex but do not share a common side
□ a pair of same - side interior angles formed by a transversal intersecting parallel lines

Explanation:

Supplementary angles add up to 180 degrees. Adjacent angles share a common side and a common vertex. A linear - pair is adjacent and supplementary, so it's not a counter - example. Vertical angles can be supplementary in some cases but are not adjacent. Non - vertical angles formed by two intersecting lines may or may not be supplementary or adjacent. Two right angles that share a vertex but not a side are supplementary but not adjacent. Same - side interior angles formed by a transversal intersecting parallel lines are supplementary but not always adjacent.

Answer:

B. A pair of vertical angles
C. A pair non - vertical angles formed by two intersecting lines
D. Two right angles that share a common vertex but do not share a common side
E. A pair of same - side interior angles formed by a transversal intersecting parallel lines