1999 AMC 8 Problems/Problem 21
Contents
Problem
The degree measure of angle is
Solution
Solution 1
Angle-chasing using the small triangles:
Use the line below and to the left of the angle to find that the rightmost angle in the small lower-left triangle is .
Then use the small lower-left triangle to find that the remaining angle in that triangle is .
Use congruent vertical angles to find that the lower angle in the smallest triangle containing is also .
Next, use line segment to find that the other angle in the smallest triangle containing is .
The small triangle containing has a angle and an angle. The remaining angle must be
Solution 2
The third angle of the triangle containing the angle and the angle is . It follows that is the third angle of the triangle consisting of the found angle and the given angle. Thus, is a angle, and so the answer is .
Video Solution by OmegaLearn
https://youtu.be/suaYxFnoU6E?t=99
~ pi_is_3.14
See Also
1999 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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