Question
Vertical angles must: Check all that apply. \( \square \) A. be congruent. \( \square \) B. have the same vertex. \( \square \) C. be complementary. D. be acute.
Ask by Ruiz Rose. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Vertical angles must be congruent and have the same vertex.
Solution
Vertical angles are formed when two lines intersect, creating two pairs of opposite angles. Let's evaluate each option:
- **A. be congruent.**
- **True.** Vertical angles are always congruent, meaning they have equal measures.
- **B. have the same vertex.**
- **True.** Vertical angles share the same vertex where the two lines intersect.
- **C. be complementary.**
- **False.** Complementary angles sum to 90 degrees. Vertical angles are congruent, so they sum to 180 degrees only if each is 90 degrees. However, vertical angles can be any pair of congruent angles, not necessarily complementary.
- **D. be acute.**
- **False.** Vertical angles can be acute or obtuse depending on the intersecting lines. There's no requirement for them to be acute.
**Correct Answers:**
**A. be congruent.**
**B. have the same vertex.**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
Vertical angles are a fascinating aspect of geometry! They are formed when two lines intersect, creating pairs of opposite angles that share a vertex. The amazing part is that these angles are always congruent (meaning they have equal measures), making option A a true statement. Additionally, it’s essential for these angles to have the same vertex, which means option B is also correct! However, vertical angles don’t have to be complementary (adding up to 90 degrees), and they certainly aren’t restricted to being acute (less than 90 degrees). So stick with A and B for your checkboxes!
