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3 years ago

What are the values of x and y in this figure?

Mathematics

1 answer:

Reika [66]3 years ago

6 0

Hello!

We know that the sum of all angles in a triangle is 180 degrees. This can be represented by the following formula:

(angle 1) + (angle 2) + (angle 3) = 180

Insert all known values and variables of triangle ABC into the formula above:

30 + (80 + y) + y = 180

Simplify and combine like terms:

30 + 80 + y + y = 180
110 + 2y = 180

Now subtract 110 from both sides of the equation:

2y = 70

Divide both sides by 2:

y = 35

We have now proven that Y is equal to 35 degrees. Using the known value of Y, we can find the value of X using the same formula as above. Begin by inserting all known values and variables of triangle BCD:

y + y + x = 180
(35) + (35) + x = 180

Combine like terms:

70 + x = 180

Subtract 70 from both sides of the equation:

x = 110

We have now proven that X is equal to 110 degrees. Therefore, considering the known values of X and Y, the answer to this problem is C.

I hope this helps!

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3 years ago

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puteri [66]

Answer:

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Step-by-step explanation:

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3 years ago

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katovenus [111]

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3 years ago

The coordinates of parallelogram UVWZ are U(a, 0), W(c - a, b), and Z(c, 0). Find the coordinates of V without using any new var

UkoKoshka [18]

Check the picture below.

so, as you can see, the UV segment is parallel to ZW, and therefore, they're the same slope, hmmm wait just a second, what is the slope of ZW anyway?

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&Z&(~ c &,& 0~) 
% (c,d)
&W&(~ c-a &,& b~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{b-0}{(c-a)-c}\implies \cfrac{b}{-a}$

since now we know the ZW slope, we also know what is the slope for UV, thus,

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&U&(~ a &,& 0~) 
% (c,d)
&V&(~ x &,& y~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{y-0}{x-a}~~=~~\stackrel{ZW's~slope}{\cfrac{b}{-a}}
\\\\\\
\begin{cases}
y-0=b\implies \boxed{y=b}\\
-----------\\
x-a=-a\implies \boxed{x=0}
\end{cases}\qquad \qquad V~(0,b)$

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3 years ago