# Point D on side AB of triangle ABC is chosen so that AD = AC. It is known that ∠CAB = 54 ° and ∠ACB = 104 °. Find the angle of the DCB.

May 31, 2020 | Education

| Consider the triangle ACD.

By the theorem on the sum of the angles of a triangle:

180 ° = ∠CAB + ∠ADC + ∠ACD

180 ° = 54 ° + ∠ADC + ∠ACD

∠ADC + ∠ACD = 126 °

Since AD = AC, this triangle is isosceles.

Then, ∠ADC = ∠ACD (by the property of an isosceles triangle), we obtain that:

∠ADC = ∠ACD = 126 ° / 2 = 63 °

∠DCB = ∠ACB-∠ACD = 104 ° -63 ° = 41 °

Answer: 41

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