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:60°60°60° ΔASDDSE AED=CAE=20=20

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