Angles are measured in degrees, using a protractor. There are 360° in a circle, and 90° in a right angle. A triangle has a total of 180° in its three inner angles, so that if the size of two angles is known, it is always possible to work out the third. Since pairs of inner and outer angles must add up to 360°, it is also possible to work out the inner angles if two of the outer angles are known.
The concept of angle is one of the most important concepts in geometry. The concepts of equality, sums, and differences of angles are important and used throughout geometry, but the subject of trigonometry is based on the measurement of angles.
Angles: 15, 30, 45 degrees.
There are two commonly used units of measurement for angles. The more familiar unit of measurement is that of degrees. A circle is divided into 360 equal degrees, so that a right angle is 90°. we’ll only consider angles between 0° and 360°.
Degrees may be further divided into minutes and seconds, but that division is not as universal as it used to be. Each degree is divided into 60 equal parts called minutes. So seven and a half degrees can be called 7 degrees and 30 minutes, written 7° 30′. Each minute is further divided into 60 equal parts called seconds, and, for instance, 2 degrees 5 minutes 30 seconds is written 2° 5′ 30″. The division of degrees into minutes and seconds of angle is analogous to the division of hours into minutes and seconds of time.
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