∠AOB等于90度,∠AOC是锐角,OD平分∠BOC,OE平分∠AOC,求∠DOE的度数
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发布时间:2024-10-11 03:33
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时间:2024-11-07 12:09
设∠boe
=
α
∠aod=
β
∠aoe=δ
∠doe=θ
∵∠aoc为锐角,od平分∠aoc,oe平分∠boc.
∴∠boe
=∠eoc=
α
∠aod=∠doc=
β
又∵∠eoc=
∠aod
+
∠doc
+
∠aoe
=
2β
+
δ
=
α
∴
∠aob=
90°
=
∠boe+∠aoe
=
α
+
δ
=
2β
+
2δ
∴
∠doe=
θ
=
β
+
δ
=
1/2
∠aob
=
45°
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