Question

1. mai says that angles a and b are vertical angles and complementary angles. tyler says that angles c and d are vertical angles and supplementary angles. who is correct? explain your thinking.

Explanation:

1. For Mai's claim: Vertical angles are opposite angles formed by intersecting lines, which are equal. Angles $a$ and $b$ are adjacent (share a side) and form a right angle, so they are complementary, not vertical.
2. For Tyler's claim: Supplementary angles add to $180^\circ$. Angles $c$ and $d$ are vertical angles (opposite each other at the intersection), so they are equal. Since angle $d$ is a right angle ($90^\circ$), $c$ is also $90^\circ$, and their sum is $180^\circ$, so they are supplementary.

Answer:

Tyler is correct. Mai is wrong because angles $a$ and $b$ are complementary (they form a $90^\circ$ angle) not vertical angles. Tyler is correct because angles $c$ and $d$ are both $90^\circ$, so their sum is $180^\circ$, making them supplementary angles.