Question

if the bisectors of two adjacent angles A and B of a quadrilateral ABCD intersect at a point O such that angle C + angle D equals to ke angle AOB, then find the value of k.​

Answer 1

Answer:

good time for a while since I've been able too much

Answer 2

First of all, you have to know these two rules:

∠A + ∠B + ∠C + ∠D = 360 (For four angles and four sides)

∠A + ∠B + ∠AOB = 180 (for triangles)

∠AOB = 180 - [(∠A +∠B)/2]

∠C + ∠D = k. ∠AOB, where ∠AOB = 180 - [(∠A +∠B)/2]

So, ∠C + ∠D = k. [(360 - [ ∠A + ∠B] )/2]

2[∠C + ∠D]= k. (360 - [ ∠A + ∠B] ), where ∠C + ∠D = 360- (∠A + ∠B)

2[360-(∠A + ∠B)] = k. (360 - [ ∠A + ∠B])

By dividing both sides by (360 - [ ∠A + ∠B]) we will get:

2=k or k=2.

Hope it is helpful!