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Chapter 10: Problem 65

What is an angle and what determines its size?

Short Answer

Expert verified
An angle is defined by two rays meeting at a common point, known as a vertex. The size of the angle is determined by the amount of rotation one arm has to go to coincide with the other and can be measured in degrees or radians. A straight line forms an angle of 180 degrees or \(\pi\) radians, a complete cycle forms an angle of 360 degrees or 2\(\pi\) radians.

Step by step solution

01

Define an Angle

An angle is formed when two rays meet at a point, also known as the vertex. The rays are referred to as the arms or sides of the angle.
02

Explain Size Determination

The size of an angle is determined by the amount of rotation one arm has to undergo to coincide with the other arm, and it is measured either in degrees or radians. An angle that measures 180 degrees is a straight line, while an angle that measures 360 degrees forms a complete rotation. A smaller angle (less than 90 degrees) is an acute angle, exactly 90 degrees is a right angle, and larger than 90 but less than 180 is an obtuse angle.
03

Discuss Radians

In the radian system of measurement, an angle's measurement is the length of the arc made by sweeping out the angle on a circle of radius one. Therefore, a full rotation (360 degrees) is equivalent to 2\(\pi\) radians.

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