Question

In the given figure AB ∥ CD, ∠BDC=80°.∠BOC= 115° Find ∠CAB.

Answer 1

Answer:

The answer to the question is ∠CAB = 35°.

Step-by-step explanation:

The given:

→ AB and CD are parallel

→ ∠BDC=80°

→ ∠BOC= 115°

To find out:

→ ∠CAB

Solution:

→ In the figure, we can see that BD and AC are straight lines. We know that the total angle in a straight line is 180°. Therefore, we can find the angles COD and AOB by the following steps,

⇒ In the case of BD

    ∠BOC + ∠COD = 180°

     115° + ∠COD = 180°

      ∠COD = 180° - 115°

               = 65°

⇒  In the case of AC

    ∠BOC + ∠AOB = 180°

     115° + ∠AOB = 180°

      ∠AOB = 180° - 115°

               = 65°

→ The sum of the three angles in a triangle is 180°. Consider the triangle OCD,

    ∠OCD + ∠ODC + ∠COD = 180°

     ∠OCD + 80° + 65° = 180°

      ∠OCD + 145° = 180°

      ∠OCD = 180° - 145°

                = 35°

→ In the figure, ∠CAB and ∠OCD are corresponding angles. And we know that the corresponding angles are always equal. Therefore,

          ∠CAB = ∠OCD

 Hence, ∠CAB = 35°