ABCD – a rhombus whose diagonals intersect at point O, calculate the degree measure of the outer angle

ABCD – a rhombus whose diagonals intersect at point O, calculate the degree measure of the outer angle of the triangle AOB with apex at point B, if the angle CAD = 28 °

The diagonals of the rhombus are the bisectors of the angles of the rhombus at its vertices, then the angle CAB = CAD = 28.

Since the diagonals of the rhombus intersect at right angles, the angle AOB = 90, then in a right-angled triangle AOB the angle ABO = 180 – AOB – BAO = 180 – 90 – 28 = 62.

The external angle MBC of the triangle ABO is adjacent to the corners ABO. Since the sum of adjacent angles is 180, the angle MBC = 180 – ABO = 180 – 62 = 118.

Answer: The outer angle of triangle AOB at vertex B is 118.