SLG_M1_5.5.6 LEOV-Select Appropriate Algebraic Notation PDF

Subject Code M1 Elementary Algebra Module Code 5.0 Linear Equations in One Variable (LEOV) Lesson Code 5.5.6 Problem Solving Involving LEOV (Select Appropriate Algebraic Notation) Time Limit 30 minutes IGNITE 15 m...

Subject Code M1 Elementary Algebra Module Code 5.0 Linear Equations in One Variable (LEOV) Lesson Code 5.5.6 Problem Solving Involving LEOV (Select Appropriate Algebraic Notation) Time Limit 30 minutes IGNITE 15 minutes [Actual Time Allotment _____ mins] In the previous lesson, the geometry word problems involved the circumference and area of circle, and the perimeter of a triangle. For this lesson, it will involve angles and angles in a triangle. Sum of the Angles of a Triangle 𝑚∠1 + 𝑚∠2 + 𝑚∠3 = 180⁰ Example 1 In a right triangle, apart from the right angle, the measure of the other angle is twice the measure of the other angle. Find the angles of the triangle. Step 1 Facts about the triangle: a) It is a right triangle. b) The measure of the other angle is twice as the other angle. Step 2 Represent the unknown: Let 𝑥 = 2𝑛𝑑 𝑎𝑛𝑔𝑙𝑒 2𝑥 = 3𝑟𝑑 𝑎𝑛𝑔𝑙𝑒 Step 3 Make an equation: 𝑚∠1 + 𝑚∠2 + 𝑚∠3 = 180 90 + 𝑥 + 2𝑥 = 180 Step 4 Solve: 90 + 𝑥 + 2𝑥 = 180 90 + 3𝑥 = 180 Combine like terms 3𝑥 = 180 − 90 Transpose 3𝑥 = 90 Combine like terms 3𝑥 90 3 = 3 Division Property of Equality 𝑥 = 30⁰ Division Fact If 𝑥 = 30, where x is the 2nd angle, then the measure of the 3rd angle is 2(30) = 60. Math 1 Page 1 of 6 Step 5 The measures of the angles of the right triangle are 30⁰, 60⁰, and 90⁰. Check the answer. The answer should satisfy all the given facts. a.) The triangle is a right triangle one angle measures 90⁰ b.) The measure of the other angle is twice as the other angle. 60 = 2(30) 60 = 60 Complementary Angles – two angles whose sum is 90⁰. 𝑚∠1 + 𝑚∠2 = 90⁰ Example 2 The measure of an angle is 16⁰ more than its complement. What are the measures of the angles? Step 1 Facts about the angles: a) Two angles are complementary. b) One angle measures 16⁰ more than its complement. Step 2 Represent the unknown: Let 𝑥 = 𝑐𝑜𝑚𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦 𝑎𝑛𝑔𝑙𝑒 𝑥 + 160 = 𝑜𝑛𝑒 𝑎𝑛𝑔𝑙𝑒 Step 3 Make an equation: 𝑚∠1 + 𝑚∠2 = 90⁰ 𝑥 + 𝑥 + 16 = 90 Step 4 Solve: 𝑥 + 𝑥 + 16 = 90 2𝑥 + 16 = 90 Combine like terms 2𝑥 = 90 − 16 Transpose 2𝑥 = 74 Combine like terms 2𝑥 74 = Division Property of Equality 2 2 𝑥 = 37 Division Fact If 𝑥 = 37, where x is the complementary angle, then the measure of the other angle is 37 + 16 = 53. Math 1 Page 2 of 6 Step 5 The measures of the complementary angles are 37⁰ and 53⁰. Check the answer. The answer should satisfy all the given facts. a) The angles are complementary 37 + 53 = 90 90 = 90 b) One angle measures 16⁰ more than its complement 53 = 37 + 16 53 = 53 Supplementary Angles – two angles whose sum is 180⁰. 𝑚∠1 + 𝑚∠2 = 180⁰ Example 3 Two angles are supplementary. If one angle is 12⁰ more than 6 times of the other angle, find the two angles. Step 1 Facts about the angles: a) Two angles are supplementary. b) One angle is 12⁰ more than 6 times the other. Step 2 Represent the unknown: Let 𝑥 = other angle 6𝑥 + 12 = one angle Step 3 Make an equation: 𝑚∠1 + 𝑚∠2 = 180 𝑥 + 6𝑥 + 12 = 180 Step 4 Solve: 𝑥 + 6𝑥 + 12 = 180 7𝑥 + 12 = 180 Combine like terms 7𝑥 = 180 − 12 Transpose 7𝑥 = 168 Combine like terms 7𝑥 168 7 = 7 Division Property of Equality 𝑥 = 24 Division Fact If 𝑥 = 24, where x is the measure of one angle, then the measure of its supplement is 180 − 24 = 156. Math 1 Page 3 of 6 Step 5 The measures of the supplementary angles are 24⁰ and 156⁰. Check the answer. The answer should satisfy all the given facts. a) The angles are supplementary 24 + 156 = 180 180 = 180 b) One angle is 12⁰ more than 6 times the other 156 = 6(24) + 12 156 = 156 NAVIGATE 15 minutes [Actual Time Allotment _____ mins] Even-numbered items may be graded. Odd-numbered items have answers at the end of the lesson. For submission of answers to even-numbered items and grading scheme, consult your teacher. Instructions: Read and understand each problem carefully. Answer it by selecting appropriate algebraic notation following the five steps. 1. In a triangle, the second angle is 7° greater than the first angle. If the third angle is 3° less than twice the first angle, find the three angles of the triangle. 2. Izzie wants to fence her triangular garden. The two sides of her garden have the same length while the third side is 32 cm less than twice as the other sides. The perimeter of Izzie’s garden is 220 cm. What are the dimensions of Izzie’s garden? (Note: The garden forms an isosceles triangle.) Math 1 Page 4 of 6  3. The sum of the complement and supplement of an angle is thrice the given angle. Find the angle. 4. The supplement of a given angle is 10 degrees less than thrice the complement of the same angle. Find the measure of the given angle. KNOT Points to Remember! Five Steps in Solving Real-Life Word Problems by Selecting an Appropriate Algebraic Notation: Step 1: Read and understand the problem. Step 2: Represent the unknown. Step 3: Make an appropriate equation. Step 4: Solve. Step 5: Interpret and check. Math 1 Page 5 of 6 REFERENCES Albarico, J.M. (2013). THINK Framework. Based on Ramos, E.G. and N. Apolinario. (n.d.) Science LINKS. Quezon City: Rex Bookstore Inc. Fair, J., et. al. (1995). Algebra 1. Prentice Hall : New Jersey Oronce, O.A. and Mendoza, M.O.(2003). Exploring Mathematics:Elementary Algebra I. Quezon City: Rex Book Store Inc. Retrieved from https://www.onlinemathlearning.com/geometry-math-problems.html Retrieved from https://www.onlinemath4all.com/complementary-and-supplementary-angles-word- problems.html Prepared by: JOANE C. DALISAY Reviewed by: MARIO DANILO R. LLANURA Position: SST-III Position: SST-III Campus: PSHS-MRC Campus: PSHS-MC ANSWERS TO ODD-NUMBERED ITEMS: Item Step 1 Step 2 Step 3 Step 4 Step 5 Number 1 a) second angle is 7° 𝑥 = 1st angle 𝑥 + (𝑥 + 7) 4𝑥 + 4 = 180 The measures of the three greater than the 𝑥 + 7 = 2nd + (2𝑥 − 3) 4𝑥 = 176 angles are 44, 51, and first angle angle = 180 𝑥 = 44 85. 2𝑥 − 3 = 3rd b) the third angle is angle If the measure of Checking: 3° less than twice the 1st angle is a) second angle the first angle 44, then the 2nd 51 = 44 + 7 and the 3rd angles are 44 + 7 = 51 b) third side and 2(44) − 3 = 85 = 2(44) − 3 85, respectively. c) sum 44 + 51 + 85 = 180 3 a) sum of the 𝑥 = angle (90 − 𝑥) 270 − 2𝑥 = 3𝑥 The measure of the angle complement and 90 − 𝑥 = + (180 − 𝑥) 270 = 5𝑥 is 54. supplement of an complement = 3𝑥 𝑥 = 54 angle is thrice 180 − 𝑥 = Checking: the given angle supplement If the measure of a) 36 + 126 = 162 the angle is 54, = 3(54) then its complement is 90 − 54 = 36 and its supplement is 180 − 54 = 126. 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