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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