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# Solving word problems ~ complementary and supplementary angles

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### Solving word problems ~ complementary and supplementary angles

1. 1. Solving Word Problems <ul><ul><ul><li>Represent </li></ul></ul></ul><ul><ul><ul><li>Translate </li></ul></ul></ul><ul><ul><ul><li>Solve </li></ul></ul></ul><ul><ul><ul><li>Interpret </li></ul></ul></ul><ul><ul><ul><li>Check </li></ul></ul></ul>
2. 2. Complementary Angles
3. 3. <ul><li>Let: angle  x </li></ul><ul><li>complement  90 – x </li></ul>The angle is 36° more than its complement. angle x x x + x 2x x comp + 36 (90 – x) + 36 90 – x + 36 90 + 36 126 63 = = = = = =  63°  27°
4. 4. <ul><li>Let: angle  x </li></ul><ul><li>complement  90 – x </li></ul>The angle is 14° less than its complement. angle x x x + x 2x x comp – 14 (90 – x) – 14 90 – x – 14 90 – 14 76 38 = = = = = =  38°  52°
5. 5. <ul><li>Let: angle  x </li></ul><ul><li>complement  90 – x </li></ul>The angle is thrice its complement. angle x x x + 3x 4x x 3  comp 3 (90 – x) 270 – 3x 270 270 67.5 = = = = = =  67.5°  22.5°
6. 6. <ul><li>Let: angle  x </li></ul><ul><li>complement  90 – x </li></ul>The angle is 57° more than twice its complement. angle x x x + 2x 3x x 2  comp + 57 2 (90 – x) + 57 180 – 2x + 57 180 + 57 237 79 = = = = = =  79°  11°
7. 7. <ul><li>Let: angle  x </li></ul><ul><li>complement  90 – x </li></ul>The angle is 275° less than four times its complement. angle x x x + 4x 5x x 4  comp – 275 4 (90 – x) – 275 360 – 4x – 275 360 – 275 85 17 = = = = = =  17°  83°
8. 8. Supplementary Angles
9. 9. <ul><li>Let: angle  x </li></ul><ul><li>supplement  180 – x </li></ul>The angle is 98 more than its supplement. angle x x x + x 2x x supp + 98 (180 – x) + 98 180 – x + 98 180 + 98 278 139 = = = = = =  139°  51°
10. 10. <ul><li>Let: angle  x </li></ul><ul><li>supplement  180 – x </li></ul>The angle is 74° less than its supplement. angle x x x + x 2x x supp – 74 (180 – x) – 74 180 – x – 74 180 – 74 106 53 = = = = = =  53°  127°
11. 11. <ul><li>Let: angle  x </li></ul><ul><li>supplement  180 – x </li></ul>The angle is twice its supplement. angle x x x + 2x 3x x 2  supp 2 (180 – x) 360 – 2x 360 360 120 = = = = = =  120°  60°
12. 12. <ul><li>Let: angle  x </li></ul><ul><li>supplement  180 – x </li></ul>The angle is 84° more than thrice its supplement. angle x x x + 3x 4x x 3  supp + 84 3 (180 – x) + 84 540 – 3x + 84 540 + 84 624 156 = = = = = =  156°  24°
13. 13. <ul><li>Let: angle  x </li></ul><ul><li>supplement  180 – x </li></ul>The angle is 123° less than twice its supplement. angle x x x + 2x 3x x 2  supp – 123 2 (180 – x) – 123 360 – 2x – 123 360 – 123 237 79 = = = = = =  79°  101°
14. 14. (mixed)
15. 15. <ul><li>Let: angle  x </li></ul><ul><li>complement  90 – x </li></ul><ul><li>supplement  180 – x </li></ul>The supplement of an angle is 126° more than twice its complement. supp (180 – x) 180 – x – x + 2x x 2  comp + 126 2 (90 – x) + 126 180 – 2x + 126 180 + 126 – 180 126 = = = = =  126°  none  54
16. 16. <ul><li>Let: angle  x </li></ul><ul><li>complement  90 – x </li></ul><ul><li>supplement  180 – x </li></ul>The complement of an angle is 326° less than thrice its supplement. comp (90 – x) 90 – x – x + 3x 2x x 3  supp – 326 3 (180 – x) – 326 540 – 3x – 326 540 – 326 – 90 124 62 = = = = = =  62°  28°  118°
17. 17. <ul><li>Let: angle  x </li></ul><ul><li>complement  90 – x </li></ul><ul><li>supplement  180 – x </li></ul>The sum of the complement and the supplement of an angle is 148°. comp + supp (90 – x) + (180 – x) 90 – x + 180 – x 90 + 180 – 148 122 61 148 148 148 x + x 2x x = = = = = =  61°  29°  119°
18. 18. <ul><li>Let: angle  x </li></ul><ul><li>complement  90 – x </li></ul><ul><li>supplement  180 – x </li></ul>Twice the complement of an angle is 300° less than thrice its supplement. 2  comp 2 (90 – x) 180 – 2x – 2x + 3x x 3  supp – 300 3 (180 – x) – 300 540 – 3x – 300 540 – 300 – 180 60 = = = = =  60°  30°  120°
19. 19. Answer the following:
20. 20. Find the measure of an angle if: <ul><li>it is 30° more than twice its supplement </li></ul><ul><li>it is 62° less than thrice its complement. </li></ul><ul><li>its complement is 46 ° more than thrice the supplement. </li></ul><ul><li>its supplement and complement add up to 170 ° . </li></ul><ul><li>thrice its complement is 150° less than twice its supplement. </li></ul>
21. 21. <ul><li>BONUS: The sum of thrice the complement and twice the supplement is 50 more than twice the sum of the complement and supplement. </li></ul>
22. 22. Assignment. Find the measure of  R if: <ul><li>it is 50° more than its complement. </li></ul><ul><li>it is 12° less than its complement. </li></ul><ul><li>it is thrice its complement. </li></ul><ul><li>it is half its complement. </li></ul><ul><li>it is 58° more than thrice its complement. </li></ul><ul><li>it is twice the measure of its supplement. </li></ul><ul><li>it is 44° less than its supplement. </li></ul><ul><li>its supplement is thrice its complement. </li></ul><ul><li>its complement and supplement add up to 120 ° . </li></ul><ul><li>its complement is 90° less than its supplement. </li></ul>