Solving Word Problems1. Represent2. Translate3. Solve4. Interpret5. Check

Complementary Angles

Let: angle xcomplement 90 – x

The angle is 36° more than its complement.

anglexx

x + x2x

x

comp + 36(90 – x) + 36 90 – x + 3690 + 3612663

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63° 27°

Let: angle xcomplement 90 – x

The angle is 14° less than its complement.

anglexx

x + x2x

x

comp – 14(90 – x) – 1490 – x – 1490 – 147638

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38° 52°

Let: angle xcomplement 90 – x

The angle is thrice its complement.

anglexx

x + 3x4x

x

3comp3 (90 – x)270 – 3x27027067.5

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67.5° 22.5°

Let: angle xcomplement 90 – x

The angle is 57° more than twice its complement.

anglexx

x + 2x3x

x

2comp + 572 (90 – x) + 57180 – 2x + 57180 + 5723779

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79° 11°

Let: angle xcomplement 90 – x

The angle is 275° less than four times its complement.

anglexx

x + 4x5x

x

4comp – 2754 (90 – x) – 275360 – 4x – 275360 – 2758517

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17° 83°

Supplementary Angles

Let: angle xsupplement 180 – x

The angle is 98 more than its supplement.

anglexx

x + x2x

x

supp + 98(180 – x) + 98 180 – x + 98180 + 98278139

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139° 51°

Let: angle xsupplement 180 – x

The angle is 74° less than its supplement.

anglexx

x + x2x

x

supp – 74(180 – x) – 74180 – x – 74180 – 7410653

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53° 127°

Let: angle xsupplement 180 – x

The angle is twice its supplement.

anglexx

x + 2x3x

x

2supp2 (180 – x)360 – 2x360360120

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120° 60°

Let: angle xsupplement 180 – x

The angle is 84° more than thrice its supplement.

anglexx

x + 3x4x

x

3supp + 843 (180 – x) + 84540 – 3x + 84540 + 84624156

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156° 24°

Let: angle xsupplement 180 – x

The angle is 123° less than twice its supplement.

anglexx

x + 2x3x

x

2supp – 1232 (180 – x) – 123360 – 2x – 123360 – 12323779

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79° 101°

(mixed)

Let: angle xcomplement 90 – xsupplement 180 – x

The supplement of an angle is 126° more than twice its complement.

supp(180 – x)

180 – x – x + 2x

x

2comp + 1262 (90 – x) + 126180 – 2x + 126 180 + 126 – 180126

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126° none 54

Let: angle xcomplement 90 – xsupplement 180 – x

The complement of an angle is 326° less than thrice its supplement.

comp(90 – x)

90 – x – x + 3x

2xx

3supp – 3263 (180 – x) – 326540 – 3x – 326540 – 326 – 9012462

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62° 28° 118°

Let: angle xcomplement 90 – xsupplement 180 – x

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

12261

148148148x + x2xx

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61° 29° 119°

Let: angle xcomplement 90 – xsupplement 180 – x

Twice the complement of an angle is 300° less than thrice its supplement.

2comp2 (90 – x)180 – 2x – 2x + 3x

x

3supp – 3003 (180 – x) – 300540 – 3x – 300540 – 300 – 18060

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60° 30° 120°

Answer the following:

Find the measure of an angle if:a) it is 30° more than twice its supplementb) 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) it is 50° more than its complement.b) it is 12° less than its complement.c) it is thrice its complement.d) it is half its complement.e) it is 58° more than thrice its complement. f) it is twice the measure of its supplement.g) it is 44° less than its supplement.h) its supplement is thrice its complement.i) its complement and supplement add up to 120°.j) its complement is 90° less than its supplement.