Question

In the given figure, AB|| CD. If ABO = 45° and COD = 100°, then find ODC​

Answer 1

Answer:

Since, ABllCD

angleB=angleC= 45°.

angleC+angleO+angleD=180.

45°+100°+angleD=180°.

angleD= 180-145.

angleD= 35°.

Answer 2

Given,

AB║CD

∠ABO = 45°

∠COD = 100°

To find,

We have to find the measure of ∠ODC.

Solution,

The measure of the ∠ODC is 35.

We can simply find the measure of ∠ODC by using the concepts of parallel lines.

AB║CD and BC is transversal line,

∠ABO = 45° (given)

∠ABC = ∠BCD ( alternate interior angles)

∠BCD = 45°

∠OCD = 45°

∠COD = 100° ( given)

In ΔCOD,

  ∠ COD + ∠ ODC + ∠OCD = 180° (Angle sum property)

              100° + ∠ODC + 45° = 180°

                                   ∠ODC = 180° - 100°-45°

                                    ∠ODC = 35°

Hence, the measure of the ∠ODC is 35°.