An Angle Sum from Trisection Points

Problem

figure

In right triangle ABCABC, ∠C=90∘\angle C = 90^\circ and AC:CB=1:3AC : CB = 1 : 3. Points EE and DD are the two trisection points of CBCB, with EE between CC and DD. Let ∠1=∠ABC\angle 1 = \angle ABC and ∠2=∠ADC\angle 2 = \angle ADC. Prove that ∠1+∠2=45∘\angle 1 + \angle 2 = 45^\circ.

Answer

Solution

Difficulty6/10
Topicsplane geometry, trigonometry, Trigonometric Identities, Triangle Geometry

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