Question

In a quadrilateral ABCD, AO and BO are the bisectors of ∠A and ∠B respectively, then (∠C + ∠D) is equal to ______.

Options

• ∠AOB

• 2∠AOB

• 3∠AOB

• 4∠AOB

Answer 1

In a quadrilateral ABCD, AO and BO are the bisectors of ∠A and ∠B respectively, then (∠C + ∠D) is equal to 2∠AOB.

Explanation:

Since AO and BO bisect ∠A and ∠B, in triangle AOB the angles at A and B are `A/2` and `B/2`. 

So, `A/2 + B/2 + ∠AOB = 180^circ`. 

Hence, `∠AOB = 180^circ - (A + B)/2`.

The sum of the angles of a quadrilateral is A + B + C + D = 360°.

Therefore, C + D = 360° – (A + B)

= 360° – [360° – 2∠AOB]

= 2∠AOB

Thus, (∠C + ∠D) = 2∠AOB.