Question

In the given figure ∠ OAB =75°, ∠ OBA =55° & ∠OCD =100° , then, ∠ODC = ?
a X=20°

b X=25°

c X=30°

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Answer 1

Given :- In the given figure, ∠OAB is equal to 75°, ∠OBA is equal to 55° and ∠OCD is equal to 100°. Then ∠ODC is equal to ?

Solution :-

In ∆OAB, we have,

→ ∠OAB + ∠OBA + ∠AOB = 180° (By Angle sum Property.) → 75° + 55°+ ∠AOB = 180°

→ 130° + ∠AOB = 180°

→ ∠AOB = 180° - 130°

→ ∠AOB = 50°

now, as we can see that,

→ ∠COD = ∠AOB = 50° (vertically opposite Angles.)

In ∆OCD, we have,

→ ∠COD + ∠OCD + ∠ODC = 180° (By Angle sum Property.)

→ 50° + 100° + ∠ODC = 180°

→ 150° + ∠ODC = 180°

→ ∠ODC = 180° - 150°

→ ∠ODC = 30° (Ans.)

Learn more :-

In ABC, AD is angle bisector,

angle BAC = 111 and AB+BD=AC find the value of angle ACB=?

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Answer 2

Answer:

In ∆OAB, we have:

∠OAB+∠OBA+∠AOB=180° [ Sum of the angles of a triangle]

⇒75°+55°+∠AOB=180°

⇒∠AOB=50°

∴∠COD=∠AOB=50° Vertically-Opposite Angles

In ∆OCD, we have:

∠COD+∠OCD+∠ODC=180° [Sum of the angles of a triangle]

⇒50°+100°+∠ODC=180°

⇒∠ODC=30°