Section 1.5 Subtraction of Real Numbers 53 Some examples of complementary angles are shown in the following table. a b a + b 20° 70° 20° + 70° = 90° 30° 60° 30° + 60° = 90° 45° 45° 45° + 45° = 90° 50° 40° 50° + 40° = 90° x° (90 - x)° x° + (90 - x)° = 90° 40° ������������������������ Supplementary Angles Supplementary angles are two angles whose sum is 180°. Supplementary angles form a straight angle when they are adjacent to each other. A straight angle is an angle whose measure is 180°. If a and b are supplementary angles, then the sum of their measures is 180°. a + b = 180° Some examples of supplementary angles are shown in the following table. a b a + b 20° 160° 20° + 160° = 180° 30° 150° 30° + 150° = 180° 45° 135° 45° + 135° = 180° 50° 130° 50° + 130° = 180° x° (180 - x)° x° + (180 - x)° = 180° �� ������������������������ ������������������ Write a mathematical expression that represents the given situation and then find the result. 3a. The world’s coldest recorded temperature is -129°F in Vostok, Antarctica. The world’s hottest recorded temperature is 134°F in Death Valley, California. What is the difference between the hottest and coldest temperatures? 3b. Find the measure of the unknown angle of the given triangle. 3c. Find the complement and supplement of an angle whose measure is 25°. Solutions 3a. We must find the difference between the hottest and coldest temperatures. This can be translated as “hottest - coldest.” Since the hottest temperature is 134°F and the coldest is -129°F, we need to find 134 - (-129) = 134 + 129 = 263°F Therefore, the difference between the hottest and coldest temperatures is 263°F. 3b. The two known angles have measures of 90° and 40°. So, the sum of the known angles is 90° + 40° = 130°. Since the total of the three angles must equal 180°, the remaining angle is the difference of 180° and the sum of the known angles. So, a = 180° - 130° = 50° The measure of the third angle is 50°. 40° a 50° 130° 50° Vostok, Antarctica
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