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Chapter 2: Problem 7

Two angles whose measures sum to \(90^{\circ}\) are \(\longrightarrow\) angles. Two angles whose measures sum to \(180^{\circ}\) are \(\longrightarrow\) angles.

Short Answer

Expert verified
Complementary angles, Supplementary angles.

Step by step solution

01

Identify the Sum for Each Type of Angle

First, identify the sum of the angles for each type. The problem states that two angles sum to 90 degrees and another pair sum to 180 degrees.
02

Define Angles that Sum to 90 Degrees

Two angles whose measures sum to 90 degrees are called complementary angles. This is because the term 'complementary' is specifically defined for angles with this sum.
03

Define Angles that Sum to 180 Degrees

Two angles whose measures sum to 180 degrees are called supplementary angles. The term 'supplementary' is used for angles that have a sum of 180 degrees.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Complementary Angles
Complementary angles are two angles whose measures add up to 90 degrees. These angles don't have to be next to each other or form a right angle; they just need their measures to sum to 90 degrees.

  • If one angle measures 30 degrees, the other must measure 60 degrees to be complementary.
  • One common example is when two angles form a right angle, such as 45 degrees and 45 degrees.
Think of complementary angles as a 'complete' right angle. If you add any two angles and get 90 degrees, they automatically become complementary.
Supplementary Angles
Supplementary angles are two angles whose measures add up to 180 degrees. Like complementary angles, these don't necessarily need to be adjacent but often are.

  • For instance, if one angle measures 110 degrees, the other must be 70 degrees to be supplementary.
  • A straight line forms an example of supplementary angles, where two angles share a common side that aligns with the line 鈥� say 120 degrees and 60 degrees.
Imagine supplementary angles as forming a straight line. Whenever two angles sum to 180 degrees, they are supplementary, creating a line or a flat surface.
Angle Sum Properties
Angles have specific properties when summed up, giving rise to terms like complementary and supplementary. Understanding these properties helps in solving various geometric problems.

  • Complementary angles sum to 90 degrees.
  • Supplementary angles sum to 180 degrees.
Knowing these concepts helps in various applications, from finding unknown angle measures to proving geometric theorems. Considering these relationships makes it easier to approach more complex angle-related problems. For example, if you know one angle, you can quickly find its complement or supplement using subtraction: \(\ angle_{complement} = 90^\circ - angle \) or \(\ angle_{supplement} = 180^\circ - angle \).

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