MO Z7–I–6 2021

In the triangle ABC, point D lies on the AC side and point E on the BC side. The sizes of the angles ABD, BAE, CAE and CBD are 30°, 60°, 20° and 30°, respectively. Find the size of the AED angle.

Correct answer:

AED =  20 °

Step-by-step explanation:

ABD=30 BAE=60 CAE=20 CBD=30  α=CAE+BAE=20+60=80 β=ABD+CBD=30+30=60 ADB=180αABD=1808030=70 γ=180αβ=1808060=40  AEB=180BAEβ=1806060=60 ASB=180BAEABD=1806030=90  AED+BDE=90 ADB=180CAE(AED+BDE) ADB=180CAE90=1802090=70  AEC=180γCAE=1804020=120 CDB=180γCBD=1804030=110  AS=ES  ΔAEB:606060 ΔASDDSE AED=CAE=20=20

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