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MrGumby

In this example, y is equal to 8.

In order to find this, first note that the two x value expressions create a straight line. That means when we add them together they will equal 180. this will give us a value for x.

x + 10 + 10x - 61 = 180

11x - 51 = 180

11x = 231

x = 21

Now that we have the value of x, we can do the same for the straight line created by the x + 10 angle and the 18y + 5 angle.

x + 10 + 18y + 5 = 180

(21) + 10 + 18y + 5 = 180

36 + 18y = 180

18y = 144

y = 8

2134jenny

Answer:

x=21 and y=8

Step-by-step explanation:

In the figure we have a vertical line that has 180º then the sum of (10x-61)º and (x+10)º have to be equal to 180º. WIth the next process we can find x:

[tex](10x-61)^o+(x+10)^o=180^o\\10x-61^o+x+10^o=180\\11x-51^o=180^o\\11x=180^o+51^o\\11x=231^o\\x=\dfrac{231^o}{11}\\x=21^o[/tex]

Now by internal and external angles, we can see that (18y+5)º and (10x-61) are opposite angles then they have to be equal:

[tex](18y+5)^o=(10x-61)^o[/tex]

We can change x because we know that x=21º then:

[tex](18y+5)^o=(10(21)-61)^o[/tex]

[tex](18y+5)^o=(210-61)^o[/tex]

[tex]18y+5^o=(149)^o[/tex]

[tex]18y=149^o-5^o[/tex]

[tex]18y=144^o[/tex]

[tex]y=\dfrac{144^o}{18}[/tex]

[tex]y=8[/tex]

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