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sergij07 [2.7K]
1 year ago
8

Find the number of units in the length of diagonal $DA$ of the regular hexagon shown. Express your answer in simplest radical fo

rm.
Mathematics
1 answer:
LekaFEV [45]1 year ago
6 0

17.32 the number of units in the length of diagonal $DA$ of the regular hexagon.

<h3>How do you find the length of the diagonal of a regular hexagon?</h3>

Six equilateral triangles can be formed from the hexagon. The equilateral triangle has an equal length on each side. The diagonal of the hexagon is formed by joining two of the sum of the lengths of the equilateral triangles. As a result, the hexagon's diagonal is twice as long as its sides.

For a polygon, the SUM of the internal angles is:

(n-2) * 180 (n=6 for hexagon)

(6-2)*180 = 720   Thus EACH angle is :   720/6 = 120 degrees

Therefore, the triangle's main angle is 120 degrees, and its other two angles are equal.

There are 180 degrees in any triangle:  

(180-120) / 2 = 30 degrees for each of the smaller angles.

Now use the law of sines:

10/sin30 = x/(sin120)

10/(.5)  × (sqrt3 )/ 2 = x

10 sqrt 3

10/sin30  ×  sin 120  =  17.32

17.32 is the number of units in the length of diagonal $DA$ of the regular hexagon.

Learn more about hexagon here:

brainly.com/question/28016053

#SPJ4

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lara31 [8.8K]

Answer:

SAS postulate

Step-by-step explanation:

AD (common)

AC = BD (both are diameters)

Angle COD = Ange AOD (vertically opposite angles)

Angle CAD = Angle BAD (angle on the circumference is half the angle at the centre)

Therefore, ABD and DCA are congruent by SAS postulate

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A _____ has two-fold rotational symmetry.
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2 years ago
EASY BRAINLIEST PLEASE HELP!!
antoniya [11.8K]

ANSWER:

We know that angle fromed by same arc are congruent. so

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2 years ago
Read 2 more answers
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