Angles and their Measures:

Angle

An angle is formed when two rays meet at a common point called vertex. Each of these rays is called an arm of the angle. Two angles which have a common arm, a common vertex and lie on either side of the common arm are called adjacent angles.

How to measure an angle

A protractor is used to measure angles. It is the semicircular transparent instrument in the instrument box. It has a base line with a central point. The angles are marked from 0° to 180° on the edge of the semicircle from left to right and from right to left starting from the baseline. In either direction, 90° is the centre.

An angle is the opening two straight lines form when they meet. The straight lines that form an angle are called the sides of the angle. The size of the angle doesn't depend on the length of its sides.

Now, to measure an angle, we place the vertex at the center of a circle, which is called central angle. Now we measure the length of the arc -- that portion of the circumference -- that the sides intercept. We then determine what relationship that arc has to the entire circumference, which is an agreed-upon number. (In degree measure that number is 360; in radian measure it is 2π .)

There are two systems for measuring angles. One is the well-known system of degree measure. The other is the strictly mathematical system called radian measure.

Degree measure

To measure an angle in degrees, we imagine the circumference of a circle divided into 360 equal parts, and we call each of those equal parts a "degree." Its symbol is a small 0: 1° -- "1 degree." The full circle, then, will be 360°. Now there are two answers for why we are using 360 here.

First, 360 has many divisors and therefore it will have many whole number parts. Secondly, 360 is close to the number of days in the astronomical year, 365.

So, when 360° is the measure of a full circle, then 180° will be half a circle. 90° -- one right angle -- will be a quarter of a circle; and 270°will be three quarters of a circle: three right angles.

Radian measure

An angle can also be measured in radians. A Radian is the angle made by taking the radius and wrapping it along the edge of the circle:

There are 2π radians in a full circle. Now degrees are easier to use in everyday work, but radians are much better for mathematics.