2009 AMC 8 Problem 19
Attempt Problem 19 of the 2009 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 2009 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
Two angles of an isosceles triangle measure and What is the sum of the three possible values of
Answer: D
Small hint:
There are three ways the known angle and the angle can sit in an isosceles triangle.
Big hint:
Consider whether they are the equal angles, or whether one is the vertex angle.
Solution:
All the following possibilities are shown below.
In the first scenario, we get by the properties of the isosceles triangle.
In the second scenario, we get that from which we get that
From the third scenario, we get that from which we get that
The sum of these values yields
Thus, D is the correct answer.
Problem 19 in other years
- 1985 AMC 8
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