MathChapter 16: Lines and Angles
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Prompt
What forms an angle?
Answer
Two rays sharing a common endpoint.
Prompt
What is an angle's common endpoint called?
Answer
The vertex.
Prompt
In \(\angle ABC\), which letter is the vertex?
Answer
\(B\), the middle letter.
Prompt
What measure defines a right angle?
Answer
\(90^\circ\).
Prompt
What measure defines a straight angle?
Answer
\(180^\circ\).
Prompt
What is the range for an acute angle?
Answer
\(0^\circ<\theta<90^\circ\).
Prompt
What is the range for an obtuse angle?
Answer
\(90^\circ<\theta<180^\circ\).
Prompt
State the Angle Addition Postulate.
Answer
An interior ray divides a whole angle into adjacent parts whose measures add to the whole.
Prompt
What does an angle bisector do?
Answer
Divides an angle into two congruent angles.
Prompt
What relationship do vertical angles have?
Answer
They are congruent.
Prompt
What do complementary angles sum to?
Answer
\(90^\circ\).
Prompt
What do supplementary angles sum to?
Answer
\(180^\circ\).
Prompt
Must complementary angles be adjacent?
Answer
No; the definition requires only a 90-degree sum.
Prompt
Must supplementary angles be adjacent?
Answer
No; the definition requires only a 180-degree sum.
Prompt
What do adjacent angles on a straight line sum to?
Answer
\(180^\circ\).
Prompt
If an angle bisector creates one 37-degree part, what is the whole?
Answer
\(74^\circ\).
Prompt
How do you solve algebraic vertical angles?
Answer
Set the opposite-angle expressions equal, solve, then evaluate.
Prompt
A 47-degree angle is formed by intersecting lines. What is an adjacent angle?
Answer
\(133^\circ\).
Prompt
What result signals an invalid interior-angle setup?
Answer
A nonpositive measure or one inconsistent with the marked classification.
Prompt
What two-word notes prevent common angle-equation mistakes?
Answer
“Vertical: equal” and “straight: 180.”
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