Question

In the given diagram if AB || CD, ∠ABO = 118° , ∠BOD = 152° , then find the value of ∠ODC.

please help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

90°

Explanation:

Through point O draw a ray on left side of O which is || to AB & CD and take any point P on it.

Therefore,

∠ABO + ∠BOP = 180° (by interior angle Postulate)

118° + ∠BOP = 180°

∠BOP = 180° - 118°

∠BOP = 62°.... (1)

Since, ∠BOP + ∠POD = ∠BOD

Therefore, 62° + ∠POD = 152°

∠POD = 152° - 62°

∠POD = 90°.....(2)

∠POD + ∠ODC = 180° (by interior angle Postulate)

90° + ∠ODC = 180°

∠ODC = 180° - 90°

`\huge\red {\boxed {m\angle ODC = 90°}}`