Question

如图,已知A、O、E三点在一条直线上,OB平分∠AOC,∠BOD=90°，∠DOE=58° ，求∠COD的度数

准确答案是多少？

Answer 1

∵A、O、E三点在一条直线上
∴∠AOB+∠BOD+∠EOD=180∵∠BOD=90°∴∠AOB+∠EOD=90°, ∠BOC+∠COD=90∵OB平分∠AOC∴∠AOB=∠COB∴∠EOD=∠COD∵∠DOE=58°
∴∠COD=58°

Answer 2

∵ ∠AOD+∠DOE = 180
∴ ∠AOD = 180 - ∠DOE = 180 - 58 = 122
∵ ∠AOB+∠BOD = ∠AOD = 130 ∠BOD=90
∴ ∠AOB = 32
∵ ∠AOB=∠BOC=32 ∠BOC+∠COD = BOD = 90
∴ ∠COD = 58