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3 years ago

USING PARALLEL LINES Find the values of x and y. Explain your reasoning. I don’t understand

Mathematics

2 answers:

alukav5142 [94]3 years ago

8 0

Step-by-step explanation:

y=109 degrees (Vertically opposite angles)

109+x=180(sum of allied angles is equal to 180 degrees)

x =180-109

x = 71 degrees

y+65=180(angles on a straight line)

y=180-65

y= 115 degrees

x+y=180(sum of allied angles is = to 180 degrees)

x+115=180

x=65 degrees

Hope you got it

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AfilCa [17]3 years ago

7 0

Step-by-step explanation:

x=180°-109°=71° (Interior angles)

y= 71° (Alternate angles)

y= 180°- 65°=115° (Adjacent angles)

x= 65° (Corresponding angles)

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Let S be the sum of the integers 25-210:

S = 25 + 26 + 27 + … + 208 + 209 + 210

Let S₃, S₄, and S₁₂ denote the sums of the integers in S that are multiples of 3, 4, or 12, respectively. We'll also count how many terms each sum involves; it'll be useful later.

S₃ = 27 + 30 + 33 + … + 204 + 207 + 210 … … … (62 terms)

S₃ = 3 (9 + 10 + 11 + … + 68 + 69 + 70)

S₄ = 28 + 32 + 36 + … + 200 + 204 + 208 … … … (46 terms)

S₄ = 4 (7 + 8 + 9 + … + 50 + 51 + 52)

S₁₂ = 36 + 48 + 60 + … + 180 + 192 + 204 … … … (15 terms)

S₁₂ = 12 (3 + 4 + 5 + … + 15 + 16 + 17)

Let's look at S₃ :

S₃ = 3 (9 + 10 + 11 + … + 68 + 69 + 70)

By reversing the order of the sum, we get

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Of course S₃ = S₃*, I'm just calling it something else temporarily. Notice that every term in the same position of either sum adds up the same number.

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and so on. Then

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We can compute the other two sums in the same way.

S₄ = 4 (7 + 8 + 9 + … + 50 + 51 + 52)

S₄* = 4 (52 + 51 + 50 + … + 9 + 8 + 7)

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S₁₂ = 12 (3 + 4 + 5 + … + 15 + 16 + 17)

S₁₂* = 12 (17 + 16 +15 + … + 5 + 4 + 3)

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Then the sum you want is

S₃ + S₄ - S₁₂ = 10,975

We subtract S₁₂ because each of its terms is counted twice (once in S₃ and again in S₄).

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See below

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images attached showing all working

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