2009 AMC 8 Problems/Problem 19
Contents
Problem
Two angles of an isosceles triangle measure and . What is the sum of the three possible values of ?
Solution
There are 3 cases: where is a base angle with the as the other angle, where is a base angle with as the vertex angle, and where is the vertex angle with as a base angle.
Case 1: is a base angle with the as the other angle: Here, , since base angles are congruent.
Case 2: is a base angle with as the vertex angle: Here, the 2 base angles are both , so we can use the equation , which simplifies to .
Case 3: is the vertex angle with as a base angle: Here, both base angles are , since base angles are congruent. Thus, we can use the equation , which simplifies to .
Adding up all the cases, we get , so the answer is .
Video Solution
https://youtu.be/FDgcLW4frg8?t=902
~ pi_is_3.14
See Also
2009 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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All AJHSME/AMC 8 Problems and Solutions |
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