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In the figure above, eight central angles are 10°, 20°, 30°, 40°, 50°,
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Bunuel
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In the figure above, eight central angles are 10°, 20°, 30°, 40°, 50°, [#permalink] New post  23 Jan 2021, 04:17
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In the figure above, eight central angles are 10°, 20°, 30°, 40°, 50°, 60°, 70° and 80°. An octagon is made by joining 8 intersections on the circumference. What is the degree measure of the largest interior angle of the octagon?

A. 140
B. 145
C. 150
D. 160
E. 165



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Untitled.png
Untitled.png [ 20.55 KiB | Viewed 354 times ]

A circle, in order, is divided into 8 consecutive arcs of 10º, 20º, 30º, ..., 80º respectively. If The eight points are connected to form an octagon, what is the measure of the largest angle of that octagon?


As figure above shows, there are eight central angles in a circle, respectively are 10, 20, 30, ...80. An octagon yields when link the 8 intersections on the circumference. What is the measurement degree of the largest interior angle of the octagon?
A. 140
B. 145
C. 150
D. 160
E. 165
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chetan2u
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In the figure above, eight central angles are 10°, 20°, 30°, 40°, 50°, [#permalink] New post  23 Jan 2021, 05:14
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Bunuel wrote:
In the figure above, eight central angles are 10°, 20°, 30°, 40°, 50°, 60°, 70° and 80°. An octagon is made by joining 8 intersections on the circumference. What is the degree measure of the largest interior angle of the octagon?

A. 140
B. 145
C. 150
D. 160
E. 165






Now each of the line is equal to the radius and, therefore, each of the triangle so formed is an isosceles triangle.

We are looking for the SUM of two base angles that are maximum. It is going to be \(\angle ABC\)

As 10 and 20 are the least, the two equal angles will be \(\frac{180-10}{2}\) and \(\frac{180-20}{2}\) respectively.

So the largest angle will be sum of these two => \(\frac{180-10}{2}+\) \(\frac{180-20}{2}\)\(= 85+80=165. \)

E
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In the figure above, eight central angles are 10°, 20°, 30°, 40°, 50°, [#permalink] New post  23 Jan 2021, 04:57
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All the triangles formed inside the circle are isosceles type as 2 sides are radii in all the triangles. The largest angles are formed in triangles where the central angles are the smallest.

The internal angle in 10 degree triangle is 85 degrees and in 20 degree triangle is 80 degrees.

Internal angle of octagon is sum of these 2 = 165 degrees

Option E

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Re: In the figure above, eight central angles are 10°, 20°, 30°, 40°, 50°, [#permalink] New post  23 Jan 2021, 06:25
Bunuel wrote:
Image
In the figure above, eight central angles are 10°, 20°, 30°, 40°, 50°, 60°, 70° and 80°. An octagon is made by joining 8 intersections on the circumference. What is the degree measure of the largest interior angle of the octagon?

A. 140
B. 145
C. 150
D. 160
E. 165



Show Spoiler
Attachment:
Untitled.png

A circle, in order, is divided into 8 consecutive arcs of 10º, 20º, 30º, ..., 80º respectively. If The eight points are connected to form an octagon, what is the measure of the largest angle of that octagon?


As figure above shows, there are eight central angles in a circle, respectively are 10, 20, 30, ...80. An octagon yields when link the 8 intersections on the circumference. What is the measurement degree of the largest interior angle of the octagon?
A. 140
B. 145
C. 150
D. 160
E. 165

Smallest and second smallest central angles i.e. 10 and 20 would result in two isosceles triangles respectively. The common side of these two isosceles, if eliminated
would result in the angle of the octagon.
\(\frac{180-10}{2} + \frac{180-20}{2} = 165\)

Answer E.
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TarunKumar1234
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Re: In the figure above, eight central angles are 10°, 20°, 30°, 40°, 50°, [#permalink] New post  23 Jan 2021, 07:28
Highest internal angle of octane = (180-10)/2 +(180-20)/2 =85+80 = 165

So, I think E. :)
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