1.1.4 Pairs of Angles (continued) Example 4 Science Application

Four angles are named in this figure. Angles may appear to be congruent in a figure, but it cannot be assumed that angles (or any figures) are congruent unless that fact is given information. Begin by listing the given information. Then note the given information in the figure. Since ∠ 2 and ∠ 3 are congruent, each of those angles can be marked in the figure with a single curve to denote their congruency. It is also given that there are two pairs of complementary angles. ∠ 1 and ∠ 2 are complementary and ∠ 3 and ∠ 4 are complementary. Remember, the sum of two complementary angles is 90° and 90° is the measure of a right angle. So, in the figure, the angle composed of ∠ 1 and ∠ 2 can be marked as a right angle, as can the angle composed of ∠ 3 and ∠ 4. The last piece of given information is the measure of an angle. m ∠ 4 = 52° So, in the figure ∠ 4 can be labeled with 52°. Now use all of this information to find m ∠ 1, m ∠ 2, and m ∠ 3. Since ∠ 3 and ∠ 4 are complementary and m ∠ 4 = 52°, m ∠ 3 = 90° − 52° = 38°. Now that m ∠ 3 is known, m ∠ 2 can easily be found since ∠ 3 and ∠ 2 are congruent. So, m ∠ 2 = 38°. Now m ∠ 1 can be found by using the fact that ∠ 1 and ∠ 2 are complementary. So, m ∠ 1 = 90° − 38° = 52°.

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