Given a triangle ABC, AB = BC, CD is perpendicular to AB, angle B is 32 °. Find the angle ACD.
| September 18, 2021 | education
By condition, AB = BC, which means the triangle is isosceles, therefore the angles at the base of the AC are equal. ∠ВАС = ∠АСВ. Angle B = 32, then ∠BAC = ∠ACB = (180 – 32) / 2 = 740.
Consider a right-angled triangle ВDC, in which ∠DBC = 32, ∠ВDC = 90, then the angle ∠DCВ = 180 – 90 – 32 = 58.
Then the sought angle АСD = ∠АСВ – ∠DCВ = 74 – 58 = 16.
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