Question

in the figure, it is given that AB II CD. Angle ABO =50⁰ and angle CDO =40⁰. Find measure of angle BOD.​

Answer 1

• Angle BOD is 90°

Given:

• AB║CD
• ∠ABD = 50°
• ∠CDO = 40°

To find:

The value of the ∠BOD

Construction(to make it easy to find)

A parallel line (ml) is drawn to AB so, it is also parallel to CD

⇒ AB║ml║CD

Now,

Taking AB║ml, we get BO as transversal

⇒ ∠ABO = ∠BOl = 50° each

[As they are alternate interior angles. And they are equal]

Similarly,

Taking CD║ml, we get DO as transversal

⇒ ∠CDO = ∠DOl = 40° each

[As they are alternate interior angles. And they are equal]

Now,

∠BOD = ∠BOl + ∠DOl

∠BOD = 50° + 40°

∠BOD = 90°

Hence,

• ∠BOD = 90°

Answer 2

Please refer to the attachment.

Hope, it helps you.