Inside square ABCD, point N is selected so that triangle BNC is equilateral. Find angle NAD.
| September 12, 2021 | education
The BCN triangle is isosceles, therefore, all the angles of the triangle are 60.
Consider a triangle ABN, its sides AB and BN are equal, therefore, the angles at the base of AN are equal. Angle ABN = 90 – 60 = 30.
Then the angle BAN = BNA = (180 – 30) / 2 = 75.
Consider a triangle АNВ, in which the angles NАВ = NDA. Then the angle NAB = 90 – 75 = 15.
Answer: Angle NAB = 15.
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