The diagonals of square ABCP meet at point O. Calculate the angles of triangle AOB.

Given:
square ABCP,
АС and ВР – diagonals,
AC intersects with BP at point O,
Find the degree measures of the angles of the triangle AOB, that is, the angle AOB, the angle OBA, the angle BAO -?
Solution:
Consider the square ABCP. On the basis of the diagonal, the squares intersect at right angles. Then triangle AOB is right-angled. By the property of a square, the diagonals are halved by the intersection point. This means that the triangle AOB is still isosceles. Then the angle ABO = angle of the ABO. Knowing that the sum of the degree measures of the angles of a triangle is 180 degrees. We get:
angle ABO = angle ABO = (180 – 90): 2 = 90: 2 = 45 degrees.
Answer: 45 degrees; 45 degrees; 90 degrees.