In the figure above, eight central angles are 10°, 20°, 30°, 40°, 50°,

Question

https://gmatclub.com/forum/download/file.php?id=60249 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 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

chetan2u · Accepted Answer

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

fall2021 · Answer

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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unraveled · Answer

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.

TarunKumar1234 · Answer

Highest internal angle of octane = (180-10)/2 +(180-20)/2 =85+80 = 165 So, I think E.

Regor60 · Answer

Largest arc subtended by central angle is 360-10-20=

330

That same arc is subtended by an angle at the circle half of the central angle =

165

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In the figure above, eight central angles are 10°, 20°, 30°, 40°, 50°,

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In the figure above, eight central angles are 10°, 20°, 30°, 40°, 50°,

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