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

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by Preyansh

## Answers

2015-01-02T12:32:58+05:30

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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
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
2015-01-02T12:35:04+05:30

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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

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