Triangle ABC has angles measuring $40^\circ$ and $85^\circ$. Triangle XYZ has angles measuring $40^\circ$ and $55^\circ$. Are the two triangles similar?

Yes, by the AA Similarity Criterion.

No, because only one angle matches.

Only if their side lengths are equal.

There is not enough information to determine.

A right triangle, $\triangle PQR$, has one angle measuring $35^\circ$. Which of the following triangles must be similar to $\triangle PQR$?

A triangle with angles $90^\circ$ and $45^\circ$

A triangle with angles $90^\circ$ and $55^\circ$

A triangle with angles $45^\circ$ and $35^\circ$

A triangle with angles $60^\circ$ and $35^\circ$

Yes, because they share a $65^\circ$ angle.

No, because their other angles do not match.

Yes, by the AA Similarity Criterion.

There is not enough information.