Date post: | 22-May-2015 |
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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
======
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
======
38° 52°
Let: angle xcomplement 90 – x
The angle is thrice its complement.
anglexx
x + 3x4x
x
3comp3 (90 – x)270 – 3x27027067.5
======
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
======
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
======
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
======
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
======
53° 127°
Let: angle xsupplement 180 – x
The angle is twice its supplement.
anglexx
x + 2x3x
x
2supp2 (180 – x)360 – 2x360360120
======
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
======
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
======
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
=====
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
======
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
======
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
=====
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.