If all of the angles of a hexagon are congruent, then what is the measure of each angle?

Mathematics

2 answers:

erastovalidia [21]3 years ago

7 0

It should be 120°
Someone else correct me if I'm wrong.

Hope this helps!

Nastasia [14]3 years ago

4 0

he total number of internal degrees is (n-2)*180 = 4*180 = 720 degrees.
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let a = one of the congruent angles.
you have:
angles 1, 2, and 3 = a.
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if a = 2 * angle 4, then angle 4 = 1/2 * a
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if a = 1/2 * angle 5, then angle 5 = 2 * a
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we have:
angle 1 = a
angle 2 = a
angle 3 = a
angle 4 = 1/2 * a
angle 5 = 2 * a
angle 6 = 115
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since the sum of the angles is equal to 720, we have:
3*a + 2*a + 1/2*a + 115 = 720
combine like terms to get:
5.5 * a + 115 = 720
subtract 115 from both sides to get:
5.5 * a = 720 - 115 = 605
divide both sides by 5.5 to get:
a = 720/5.5 = 110
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angle 1, 2, and 3 are each 110 degrees.
angle 4 = 55 degrees
angle 5 = 220 degrees
angle 6 = 115 degrees
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the question is:
What is the measure of the smallest angle?
the answer is:
55 degrees.

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Simplify <img src="https://tex.z-dn.net/?f=%20%20%5Csqrt%7B%20-%20180%7D%20" id="TexFormula1" title=" \sqrt{ - 180} " alt="

QveST [7]

Answer: $(6\sqrt{5})i$

This is the same as saying $6i\sqrt{5}$

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Work Shown:

$\sqrt{-180} = \sqrt{-1*36*5}\\\\\sqrt{-180} = \sqrt{-1}*\sqrt{36}*\sqrt{5}\\\\\sqrt{-180} = i*6*\sqrt{5}\\\\\sqrt{-180} = 6i\sqrt{5}\\\\\sqrt{-180} = (6\sqrt{5})i\\\\$

where $i = \sqrt{-1}$

As the steps show above, the idea is to factor the radicand into smaller pieces where one of those pieces is the largest perfect square possible. In this case, 36 is the largest factor of 180 that's a perfect square. Then I used the rule $\sqrt{A*B} = \sqrt{A}*\sqrt{B}$ to break up the root.