Unformatted text preview: a) to label angles. So, for instance, we have α β One commonly used system to measure angles is degree measure. Quantities measured in degrees
are denoted by the familiar ‘◦ ’ symbol. One complete revolution as shown below is 360◦ , and parts
of a revolution are measured proportionately.2 Thus half of a revolution (a straight angle) measures
2 (360 ) = 180 , a quarter of a revolution (a right angle) measures 4 (360 ) = 90 and so on. One revolution ↔ 360◦ 180◦ 90◦ Note that in the above ﬁgure, we have used the small square ‘ ’ to denote a right angle, as is
commonplace in Geometry. Recall that if an angle measures strictly between 0◦ and 90◦ it is called
an acute angle and if it measures strictly between 90◦ and 180◦ it is called an obtuse angle.
It is important to note that, theoretically, we can know the measure of any angle as long as we
2 The phrase ‘at least’ will be justiﬁed in short order.
The choice of ‘360’ is most often attributed to the Babylonians. 10.1 Angles and their Measure 595 know the proportion it represents of entire...
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