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80 = 117.2625â—¦
Recall that two acute angles are called complementary angles if their measures add to 90â—¦ .
Two angles, either a pair of right angles or one acute angle and one obtuse angle, are called
supplementary angles if their measures add to 180â—¦ . In the diagram below, the angles Î± and Î²
are supplementary angles while the pair Î³ and Î¸ are complementary angles. Î²
Î¸
Î³ Î± Supplementary Angles Complementary Angles In practice, the distinction between the angle itself and its measure is blurred so that the sentence
â€˜Î± is an angle measuring 42â—¦ â€™ is often abbreviated to â€˜Î± = 42â—¦ .â€™ It is now time for an example.
Example 10.1.1. Let Î± = 111.371â—¦ and Î² = 37â—¦ 28 17 .
1. Convert Î± to the DMS system. Round your answer to the nearest second.
2. Convert Î² to decimal degrees. Round your answer to the nearest thousandth of a degree.
3. Sketch Î± and Î² .
4. Find a supplementary angle for Î±.
5. Find a complementary angle for Î² .
Solution.
1. To convert Î± to the DMS system, we start with 111.371â—¦ = 111â—¦ + 0.371â—¦ . Next we convert
0
0.371â—¦ 60 = 22.26 . Writing 22.26 = 22 + 0.26 , we...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, RenÃ© Descartes, Euclidean geometry

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