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Julli [10]
3 years ago
8

Find the value of x and y

Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
3 0

Answer:

x = 63 , y = 27

Step-by-step explanation:

x+ 117 make a straight line so they equal 180 degrees.

x+117 = 180

Subtract 117 from each side

x+117-117= 180-117

x =63

x and y are complementary, which means they add to 90

x+y = 90

63+y = 90

Subtract 63 from each side

63-63+y = 90-63

y = 27

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Step-by-step explanation:

we know that

we can divide the regular hexagon into 6 identical equilateral triangles

see the attached figure to better understand the problem

The approximate area of the circle is approximately the area of the six equilateral triangles

Remember that

In an equilateral triangle the interior measurement of each angle is 60 degrees

We take one triangle OAB, with O as the centre of the hexagon or circle, and AB as one side of the regular hexagon

Let

M  ----> the mid-point of AB

OM ----> the perpendicular bisector of AB

x ----> the measure of angle AOM

m\angle AOM =30^o

In the right triangle OAM

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so

\frac{a}{2r}=\frac{\sqrt{3}}{3}

we have

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substitute

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Find the area of six equilateral triangles

A=6[\frac{1}{2}(r)(a)]

simplify

A=3(r)(a)

we have

r=3\ units\\a=2\sqrt{3}\ units

substitute

A=3(3)(2\sqrt{3})\\A=18\sqrt{3}\ units^2

Therefore

The approximate are of the inscribed disk using the regular hexagon is A=18\sqrt{3}\ units^2

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3 years ago
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