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Unformatted text preview: 80 = 117.2625◦
Recall that two acute angles are called complementary angles if their measures add to 90◦ .
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 180◦ . In the diagram below, the angles α and β
are supplementary angles while the pair γ and θ are complementary angles. β
γ α Supplementary Angles Complementary Angles In practice, the distinction between the angle itself and its measure is blurred so that the sentence
‘α is an angle measuring 42◦ ’ is often abbreviated to ‘α = 42◦ .’ It is now time for an example.
Example 10.1.1. Let α = 111.371◦ and β = 37◦ 28 17 .
1. Convert α to the DMS system. Round your answer to the nearest second.
2. Convert β to decimal degrees. Round your answer to the nearest thousandth of a degree.
3. Sketch α and β .
4. Find a supplementary angle for α.
5. Find a complementary angle for β .
1. To convert α to the DMS system, we start with 111.371◦ = 111◦ + 0.371◦ . Next we convert
0.371◦ 60 = 22.26 . Writing 22.26 = 22 + 0.26 , we...
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