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23 Jan 2021, 05:17
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E
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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
Attachment:
Untitled.png [ 20.55 KiB | Viewed 3587 times ]
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
23 Jan 2021, 06:14
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Bunuel
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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General Discussion
fall2021
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23 Jan 2021, 05:57
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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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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
Posted from my mobile device
