Question

in given figure ABCD is a rectangle and diagonals intersect at O.if angle AOB=108°,Find angle ABO,angle ADO,angle OCB ​

Answer 1

Step-by-step explanation:

use angle sum property of a triangle to get the given angles

Answer 2

$\angle ABO = 36$°

$\angle ADO = 54$°

$\angle OCB = 54$°

Step-by-step explanation:

In rectangle ABCD , diagonals intersect at point O

AC = BD (diagonals of a rectangle are equal)

$\frac{1}{2} AC = \frac{1}{2} BD$

in triangle AOB (isoceles triangle)

let the angle OBA = x

$\angle AOB +\angle OAB + \angle OBA = 180$

108 +x+x = 180

2x = 180-108

2x = 72

x  = 36

$\angle OBA = \angle OAB = 36$

i.e $\angle ABO = 36$°

$\angle ABO = \angle ODC = 36$

We know that The four interior and exterior angles are 90 deg.

i.e

$\angle ODC + \angle AD0 = 90\\\\36 +\angle ADO = 90\\\angle ADO = 90- 36 = 54$

i.e $\angle ADO = 54$°

similarly ,

$\angle OAB = \angle OCD = 36\\\angle OCB +\angle OCD = 90\\\angle OCB + 36 = 90\\\angle OCB = 90-36\\\angle OCB = 54$

hence ,

$\angle ABO = 36$°

$\angle ADO = 54$°

$\angle OCB = 54$°

#Learn more:

Diagonals of rectangle ABCD intersect at O.If angle AOB = 30°, find angle COD angle OCD.

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