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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