If angles $PTQ$ and $STR$ are vertical angles and congruent, which of the following statements is true about their measures in standard position?

• A. Their measures are equal, so $\angle PTQ$ = $\angle STR$.
• B. Their measures are complementary, so $\angle PTQ$ + $\angle STR$ = 90°.
• C. Their measures are supplementary, so $\angle PTQ$ + $\angle STR$ = 180°.
• D. Their measures are unrelated in standard position.

Answer: (A)

Verified step by step guidance

1. Recall the definition of vertical angles: Vertical angles are the pairs of opposite angles made by two intersecting lines. They are always congruent, meaning their measures are equal.
2. Since angles \( \angle PTQ \) and \( \angle STR \) are vertical angles, by definition, their measures must be equal. This means \( m\angle PTQ = m\angle STR \).
3. Understand the difference between complementary and supplementary angles: Complementary angles add up to 90\degree, and supplementary angles add up to 180\degree. Vertical angles do not necessarily satisfy either of these conditions.
4. Because vertical angles are congruent, their measures are equal, not complementary or supplementary. Therefore, the correct relationship is \( m\angle PTQ = m\angle STR \).
5. Conclude that the statement 'Their measures are equal, so \( \angle PTQ = \angle STR \)' is true, while the other options about complementary, supplementary, or unrelated measures are false.