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Chapter 1: Problem 1

An angle whose measure is \(90^{\circ}\) is a(n) _____________ angle.

Short Answer

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Step by step solution

01

Identify Angle Measurement

The angle measurement is given as \(90^{\circ}\).
02

Recognize Angle by Degree

An angle having a measure of \(90^{\circ}\), which is often found when two lines are perpendicular to one another, is called a right angle.

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Key Concepts

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

Understanding Angle Measurement
Angle measurement is a fundamental concept in geometry. Angles are formed when two rays diverge from a common endpoint, also called the vertex. The size of an angle is determined by how wide these rays spread apart. This spread is quantified in degrees.
  • The unit "degree" is used to measure the exact amount of spread between the two rays.
  • A full circle is divided into 360 degrees, making a complete rotation around a point.
When angles are measured, they are typically denoted with the degree symbol \(^{\circ}\), which shows that you're talking about degrees rather than some other measurement unit like radians.
Common angles include:
  • An angle of \(90^{\circ}\) is a right angle.
  • An angle of \(180^{\circ}\) is a straight angle.
  • An angle of \(360^{\circ}\) completes a full circle.
In geometric contexts, when an angle is stated without further clarifications, it usually assumes measurement in degrees.
Exploring Perpendicular Lines
Perpendicular lines are two lines that intersect at a right angle. This means they meet to form a \(90^{\circ}\) angle with each other. This relationship is seen in many everyday structures, like the corners of a picture frame or the intersection of two streets.
  • At the point of intersection, four right angles are formed.
  • Each of these angles measures exactly \(90^{\circ}\).
  • Perpendicular lines symbolize an important geometric principle and are foundational in creating squares and rectangles.
To determine if two lines are perpendicular, you can check if the product of their slopes is \(-1\). This holds true especially in coordinate geometry.
Thus, understanding perpendicular lines involves visualizing the clear \(T\)-junction where two lines meet at a precise right angle.
Degrees in Geometry
Degrees in geometry help us quantify the size of angles. Historically, the idea of 360 degrees in a circle comes from the Babylonians, who used a base 60 number system. Geometry heavily relies on degrees because they offer a convenient way to classify angles.
Key facts about degrees include:
  • A degree is \(\frac{1}{360}\) of a full circle and is a standard measure for angles.
  • You can convert degrees to other units such as radians, where \(180^{\circ}\) equals \(\pi\) radians.
  • Degrees are used globally in various fields, including navigation, art, and architecture.
In practical geometry, knowing how to measure angles in degrees allows us to design and build various structures. It helps ensure that components fit together accurately, like tiles lining up or trusses forming a stable roof.

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