Solving Word Problems 1 2 3 4 5

Solving Word Problems 1. 2. 3. 4. 5. Represent Translate Solve Interpret Check

Complementary Angles

The angle is 36° more than its complement. Let: angle complement angle x x x+x 2 x x = = = x 90 – x comp + 36 (90 – x) + 36 90 – x + 36 90 + 36 126 63 63° 27°

The angle is 14° less than its complement. Let: angle complement angle x x x+x 2 x x = = = x 90 – x comp – 14 (90 – x) – 14 90 – x – 14 90 – 14 76 38 38° 52°

The angle is thrice its complement. Let: angle complement angle x x x + 3 x 4 x x = = = x 90 – x 3 comp 3 (90 – x) 270 – 3 x 270 67. 5° 22. 5°

The angle is 57° more than twice its complement. Let: angle complement angle x x x + 2 x 3 x x = = = x 90 – x 2 comp + 57 2 (90 – x) + 57 180 – 2 x + 57 180 + 57 237 79 79° 11°

The angle is 275° less than four times its complement. Let: angle complement angle x x x + 4 x 5 x x = = = x 90 – x 4 comp – 275 4 (90 – x) – 275 360 – 4 x – 275 360 – 275 85 17 17° 83°

Supplementary Angles

The angle is 98 more than its supplement. Let: angle supplement angle x x x+x 2 x x = = = x 180 – x supp + 98 (180 – x) + 98 180 – x + 98 180 + 98 278 139° 51°

The angle is 74° less than its supplement. Let: angle supplement angle x x x+x 2 x x = = = x 180 – x supp – 74 (180 – x) – 74 180 – x – 74 180 – 74 106 53 53° 127°

The angle is twice its supplement. Let: angle supplement angle x x x + 2 x 3 x x = = = x 180 – x 2 supp 2 (180 – x) 360 – 2 x 360 120° 60°

The angle is 84° more than thrice its supplement. Let: angle supplement angle x x x + 3 x 4 x x = = = x 180 – x 3 supp + 84 3 (180 – x) + 84 540 – 3 x + 84 540 + 84 624 156° 24°

The angle is 123° less than twice its supplement. Let: angle supplement angle x x x + 2 x 3 x x = = = x 180 – x 79° 101° 2 supp – 123 2 (180 – x) – 123 360 – 2 x – 123 360 – 123 237 79

(mixed)

The supplement of an angle is 126° more than twice its complement. Let: angle complement supplement supp (180 – x) 180 – x + 2 x x = = = x 90 – x 180 – x 126° none 54 2 comp + 126 2 (90 – x) + 126 180 – 2 x + 126 180 + 126 – 180 126

The complement of an angle is 326° less than thrice its supplement. Let: angle complement supplement comp (90 – x) 90 – x + 3 x 2 x x = = = x 90 – x 180 – x 62° 28° 118° 3 supp – 326 3 (180 – x) – 326 540 – 3 x – 326 540 – 326 – 90 124 62

The sum of the complement and the supplement of an angle is 148°. Let: angle complement supplement comp + supp (90 – x) + (180 – x) 90 – x + 180 – x 90 + 180 – 148 122 61 = = = x 90 – x 180 – x 148 148 x+x 2 x x 61° 29° 119°

Twice the complement of an angle is 300° less than thrice its supplement. Let: angle complement supplement 2 comp 2 (90 – x) 180 – 2 x + 3 x x = = = x 90 – x 180 – x 60° 30° 120° 3 supp – 300 3 (180 – x) – 300 540 – 3 x – 300 540 – 300 – 180 60

Answer the following:

Find the measure of an angle if: a) it is 30° more than twice its supplement b) it is 62° less than thrice its complement. c) its complement is 46° more than thrice the supplement. d) its supplement and complement add up to 170°. e) thrice its complement is 150° less than twice its supplement.

• BONUS: The sum of thrice the complement and twice the supplement is 50 more than twice the sum of the complement and supplement.

Assignment. Find the measure of R if: a) b) c) d) e) f) g) h) i) j) it is 50° more than its complement. it is 12° less than its complement. it is thrice its complement. it is half its complement. it is 58° more than thrice its complement. it is twice the measure of its supplement. it is 44° less than its supplement is thrice its complement and supplement add up to 120°. its complement is 90° less than its supplement.