返回题库

HMMT 十一月 2022 · 冲刺赛 · 第 9 题

HMMT November 2022 — Guts Round — Problem 9

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [7] Let ABCD be a trapezoid such that AB ∥ CD , ∠ BAC = 25 , ∠ ABC = 125 , and AB + AD = CD . Compute ∠ ADC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HMMT November 2022, November 12, 2022 — GUTS ROUND Organization Team Team ID#
解析
  1. [7] Let ABCD be a trapezoid such that AB ∥ CD , ∠ BAC = 25 , ∠ ABC = 125 , and AB + AD = CD . Compute ∠ ADC . Proposed by: Pitchayut Saengrungkongka ◦ Answer: 70 Solution: Construct the parallelogram ABED . From the condition AB + AD = CD , we get that EC = AD = EB . Thus, ◦ ◦ ◦ ◦ ∠ ADC = ∠ BEC = 180 − 2 ∠ BCE = 180 − 2 · 55 = 70 .