2014 AMC 8 Problem 15
Attempt Problem 15 of the 2014 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2014 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
15.
The circumference of the circle with center is divided into equal arcs, marked the letters through as seen below. What is the number of degrees in the sum of the angles and
Answer: C
Small hint:
Each adjacent pair of letters cuts off at the center.
Big hint:
The two relevant triangles are isosceles because their sides are radii.
Solution:
Note that each of the arcs splits the circle evenly, so they each cover
spans of these arcs, so Similarly, We also know that both triangles are isosceles since two of their sides are radii. Therefore, and Therefore,
Thus, C is the correct answer.
Problem 15 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
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- 1998 AMC 8
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