Question

4.In the following figure ,find the value of ∠ COD if, ∠ AOB=750 and AB=
CD.

Answer 1

Given:

∠AOB = 75°

AB = CD

To Find:

∠COD

Solution:

In ΔAOB and ΔCOD

AB = CD [given]

AO = CO [radius of the circle]

OB = OD [radius of the circle]

Now,

AOD≅COD

So, ∠AOD = ∠AOB

∠COD = 75°

Therefore, ∠COD = 75°.

Answer 2

Value of ∠COD is  75°  if ∠AOB = 75° and AB = CD in the given circle where O is center of the circle

Given:

• ∠AOB = 75°
• AB = CD

To Find:

• Value of ∠COD

Solution:

Side-Side-Side (SSS) Congruence Theorem

If all three sides of the first triangle are congruent to all three sides of the second triangle, then those two triangles are congruent.

If the corresponding sides and the corresponding angles of two triangles are congruent, then the triangles are congruent.

If two triangles are congruent, all their corresponding sides and angles are congruent.

In ΔAOB and ΔCOD

AB = CD       Given

AO  = CO     Radius

OB = OD      Radius

Hence ΔAOB ≅ ΔCOD     (SSS Congruence)

So corresponding angles must be equal

=> ∠AOB = ∠COD
=> 75° = ∠COD

Hence, Value of ∠COD is  75°