When constructing a regular hexagon inscribed in a circle, what is the measure of an angle formed by any two adjacent vertices o
f the hexagon and the center of the circle?
2 answers:
Answer:
Measure of angle is 60°
Step-by-step explanation:
Given when constructing a regular hexagon inscribed in a circle, we have to measure an angle formed by any two adjacent vertices of the hexagon and the center of the circle.
we have to find the measure of central angle of hexagon
Total measure of angle at centre is 360°
As polygon is given regular hexagon therefore central angle divides into six equal angles.
Hence, measure of an angle formed by any two adjacent vertices of the hexagon and the center of the circle is
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Answer:
A. 1/3
B. √10
C. -1, 1
D. √8, 6
E. congruent and opposite pairs parallel
F. perpendicular, not congruent
G. rhombus, explanation below
Step-by-step explanation:
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A.
Slope is the rise over the run. Let's look at F to G.
We are going from -1 to 2 on our x-axis (run), so our run is 3 units.
Our rise is 1 unit as we go from 2 to 3 on the y-axis.
This slope is the same for all of the sides.
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B.
We will use the distance formula (which is basically just the Pythagorean Theorem) to calculate the length of each side. Let's go between F and G again, but this distance is the same for all the sides.
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C.
The diagonals are the lines that connect the non-adjacent vertices.
Our two diagonals are FH and GE.
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<u>FH</u>
We go from x-value -1 to 1 from F to H, so our run is 2.
We go from y-value 2 to 0. so our rise is -2.
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<u>GE</u>
We go from x-value -2 to 2 from E to G, so our run is 4.
We go from y-value -1 to 3. so our rise is 4.
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D.
Let's use the distance formula on each of our diagonals.
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<u>FH</u>
<u /><u />
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<u>GE</u>
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E.
They are congruent as they all have the same length (√10) and the opposite sides are parallel as they have the same slope (1/3)
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F.
They are perpendicular diagonals as their slopes are negative reciprocals (1 and -1), and they are not congruent as they have different lengths (√8 and 6).
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G.
<u>Parallelogram-</u> quadrilateral with opposite pairs of parallel sides.
<u>Rhombus-</u> a parallelogram with four equal sides
<u>Square-</u> a rhombus with four right angles
We can see that this is a parallelogram as we saw that the opposite sides are parallel due to having the same slope, and the perpendicular diagonals show that as well. This is also a rhombus because if we use that distance formula on all the sides, it will be the same. It is not a square though because it does not have four right angles, so this is a rhombus.
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