Given a square ABCD. Point O is inside the square so that OA = OD = AD. Find the corner ABO.

Consider ΔAOD: OA = OD = AD, hence ΔAOD is an equilateral triangle.

Hence, by the property of an equilateral triangle, AOD = ODA = OAD = 60 °.

BAD = 90 °, because ABCD is a square. We have VAO = 90 – OAD = 90 – 60 = 30 °.

BOD – expanded angle, BOD = 180 °, then BOA = BOD – AOD = 180 – 60 = 120 °.

Consider ΔABO: BAO = 30 °, BOA = 120 °.

Because ABO + BAO + BOA = 180 °, we get:

ABO = 180 – BAO – BOA;

ABO = 180 – 30 – 120;

ABO = 30 °.

Answer: angle ABO = 30 °.