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HMMT 十一月 2015 · 团队赛 · 第 1 题

HMMT November 2015 — Team Round — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 3 ] Triangle ABC is isosceles, and ∠ ABC = x . If the sum of the possible measures of ∠ BAC is 240 , find x .
解析
  1. [ 3 ] Triangle ABC is isosceles, and ∠ ABC = x . If the sum of the possible measures of ∠ BAC is 240 , find x . Proposed by: Alexander Katz Answer: 20 There are three possible triangles: either ∠ ABC = ∠ BCA , in which case ∠ BAC = 180 − 2 x , ∠ ABC = 180 − x ∠ BAC , in which case ∠ BAC = x , or ∠ BAC = ∠ BCA , in which case ∠ BAC = . These sum to 2 540 − 3 x 540 − 3 x , so we have = 240 = ⇒ x = 20 . 2 2