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Chapter 1: Problem 2

An angle whose vertex is the center of a circle is a(n) __________ angle.

Short Answer

Expert verified
central

Step by step solution

01

Understand the given problem

Identify that the problem is asking for a specific type of angle in a circle, given that its vertex is at the center of the circle.
02

Define the type of angle

Recall the definition of different types of angles in the context of a circle. An angle whose vertex is at the center of the circle is known as a central angle.
03

Confirm the understanding

Verify that a central angle's defining feature is that its vertex is at the center and its sides (rays) intersect the circumference of the circle.

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Key Concepts

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

vertex definition
In geometry, a vertex is a fundamental concept. The vertex is the point where two or more lines, rays, or line segments meet. Think of it as a corner or a turning point. For angles, the vertex is the common endpoint of the two rays that form the angle.
For example, in a triangle, the points where the sides meet are called vertices. Similarly, in the case of an angle, the vertex is where the two arms (rays) of the angle come together. When we talk about angles in the context of circles, the vertex can play a very significant role. In the problem discussed, the vertex's location鈥攕pecifically at the center of the circle鈥攈elps define the type of angle.
circle geometry
Circle geometry involves understanding the various parts and properties of a circle. A circle is a perfectly round shape with all points the same distance from a central point called the center.
Key terms in circle geometry:
  • Radius: A line segment from the center of the circle to any point on the circle.
  • Diameter: A line that passes through the center of the circle, connecting two points on the circle.
  • Circumference: The distance around the circle.
  • Chord: A line segment connecting any two points on the circle, not necessarily through the center.
These parts help us describe various other elements and properties of circles, including different angle types like central angles and inscribed angles. For instance, a central angle's sides are the radii of the circle, meeting at the circle's center.
angle types
Angles can be classified in several ways depending on their measure and position.
Common types of angles include:
  • Acute Angle: Measures less than 90 degrees.
  • Right Angle: Measures exactly 90 degrees.
  • Obtuse Angle: Measures more than 90 degrees but less than 180 degrees.
  • Straight Angle: Measures exactly 180 degrees.
When we discuss angles in the context of a circle, we often refer to specific types like central angles and inscribed angles.
A central angle is an angle whose vertex is at the center of the circle, and its sides are radii that intersect the circle's circumference. Another type is the inscribed angle, which has its vertex on the circle itself and its sides as chords of the circle. Understanding these angle types helps solve problems related to circle geometry, like identifying a central angle in the initial problem.

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Most popular questions from this chapter

Find the degree measures of two positive and two negative angles that are coterminal with each given angle. $$ 300^{\circ} $$

Perform each computation without a calculator. Express the answer in degrees- minutes-seconds format. Use a calculator to check your answers. $$ \left(5^{\circ} 18^{\prime} 40^{\prime \prime}\right) / 4 $$

Find the length of the arc intercepted by the given central angle \(\alpha\) in a circle of radius \(r\). Round to the nearest tenth. $$ \alpha=1.3, r=26.1 \mathrm{~m} $$

Inscription Rock rises almost straight upward from the valley floor. From one point the angle of elevation of the top of the rock is \(16.7^{\circ} .\) From a point \(168 \mathrm{~m}\) closer to the rock, the angle of elevation of the top of the rock is \(24.1^{\circ} .\) How high is Inscription Rock? Round to the nearest tenth of a meter.

Perform the indicated operation. Express the result in terms of \(\pi\) $$ \frac{\pi}{3}+\frac{\pi}{4} $$
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