Question

The diagonals AC and BD intersect at O in a rectangle ABCD. If angle AOD = 45 degrees, find
angle DAC

Answer 1

The diagonal of a rectangle are equal and bisect each other which => OA = OD => angle OAD = angle ODA = x (let) Now in triangle OAD Angle A + angle O + angle D = 180 => x+ x + 45 = 180 => 2x = 180-45=> x = 135/2=> 67.5 => angle DAC = 67.5

Answer 2

In a rectangle the diagonals bisect each other.  Hence the triangle OAD is an Isosceles triangle.

Hence,    angle DAC + angle ADO + angle AOD = 180
  as      angle DAC = angle ADO  ,  

 angle DAC = angle ADO = (180 - 45) / 2 = 67.5 degrees