已知O为AD上一点,角AOC与角AOB互补,OM,ON分别为角AOC.角AOB的平分线,若角MON=40度,试求角AOC,角AOB的

问题描述:

已知O为AD上一点,角AOC与角AOB互补,OM,ON分别为角AOC.角AOB的平分线,若角MON=40度,试求角AOC,角AOB的

MON = 40
AON - AOM = 40
AOB/2 - AOC/2 = 40
(AOB - AOC)/2 = 40
AOB - AOC = 80 (1)
AOB + AOC = 180 (2)
(1)+(2) 解得AOB=130
AOC=50

令x,y,则依题意可得
x+y=180,
【x/2-y/2】(绝对值)=40,
解得x=130,y=50,
或x=50,y=130