Question

如图,角BOC=2角AOC,OD平分角AOB,角COD=25°,求角AOB的度数

Answer 1

∵∠cod=25°

∴∠aod=∠aoc+∠cod=∠aoc+25°

∠cob=∠dob+∠cod=∠dob+25°

∵od平分∠aob

∴∠aod=∠dob

∴∠aoc+25°=∠dob

∴∠cob=∠dob+25°=∠aoc+25°+25°=∠aoc+50°

∵∠cob=2∠aoc

∴2∠aoc=∠aoc+50°

∴∠aoc=50°

∴∠cob=100°

∴∠aob=55°+100°=150°