Question

in the given figure,ABCD is a rectangle and angle BOC=56° find angle ADO​

Answer 1

Given :-

angle BOC = 56°

we know that in a rectangle,

» there are two congruent diagonals.

» the diagonals of the rectangle bisect each other and

therefore DO = AO

now,

in ∆DOA,

• angle ADO = angle DAO (angles are equal to opposite sides since DO = AO) ------(i)

• angle DOA = 56° (vertical opposite angles)

sum of all three interior angles in a triangle = 180°

➡ angle ADO + angle DAO + angle DOA = 180°

➡ angle ADO + angle ADO + 56° = 180° (from equation (i))

➡ 2angleADO = 180° - 56°

➡ 2angleADO = 124°

➡ angle ADO = 124/2

➡ angle ADO = 62°

hence, the measure of angle ADO = 62°

Answer 2

We know that
Diagnols of rectangle are of same length and bisect each other
So, OA=OD
➡️ AOD is an isosceles triangle
So, base angles will be equal
➡️ angle ADO= angle DAO
Let angle ADO and DAO be x
Also, by vertically opposite angles,
Angle COB= angle DOA= 56
Now, by ASP,
➡️ 56+x+x=180
➡️ 2x= 180-56
➡️ x= 124/2
➡️ x= 62
So, answer is 62 degree

Hope this helps you