### In a quadrilateral ABCD, O is a point inside the quadrilateral such that AO and BO are the bisectors of ∠A and ∠B respectively. Prove that ∠AOB =

(∠C + ∠D).

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**Answer: **

(∠C + ∠D)

**Step by Step Explanation: **- Following figure shows the quadrilateral ABCD,

According to the question, AO and BO are the bisectors of ∠A and ∠B respectively.

Therefore, ∠BAO = ,

⇒ ∠ABO = - We know that the sum of all angles of a quadrilateral is equals to 360°.

Therefore, ∠A + ∠B + ∠C + ∠D = 360°

⇒ ∠C + ∠D = 360° - (∠A + ∠B) -----(1) - In ΔAOB,

∠BAO + ∠ABO + ∠AOB = 180° **[Since, we know that the sum of all three angles of a triangle is equals to 180°.]**

⇒ + + ∠AOB = 180°

⇒ ∠AOB = 180° - -

⇒ ∠AOB =

⇒ ∠AOB =

⇒ ∠AOB = **[From equation (1).]** - Hence, ∠AOB = (∠C + ∠D)