A teacher is making gift bags. Each bag is to be filled with pencils and stickers. The teacher has 24 pencils and 36 stickers. Each bag will have the same number of each item, with no item left over. for example, she could make two bags with 12 pencils and 18 stickers each.

What are the other possibilities? Explain your reasoning.

3 bags with 6 pencils and 12 stickers.

Step-by-step explanation:

3 goes into both 24 and 36 which makes this possible

3 bags with 8 pencils and 12 stickers ( 3 ⋅ 8 = 24 and 3 ⋅ 12 = 36 )

4 bags with 6 pencils and 9 stickers ( 4 ⋅ 6 = 24  and 4 ⋅ 9 = 36 )

6 bags with 4 pencils and 6 stickers ( 6 ⋅ 4 = 24 and 6 ⋅ 6 = 36 )

12 bags with 2 pencils and 3 stickers( 12 ⋅ 2 = 24 and 12 ⋅ 3 = 36 )

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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