Question

The sides AB and CD of a quadrilateral
ABCD are extended to points P and Q
respectively
Is ADQ+ CBP = A+ C? Justify.​

Answer 1

Answer:

From the figure..

ABD.... We get

<ABD + <ADB = <b - (1).........

(from properties of triangle...

ll'y from ∆BCD

<CBD + <CDB = <a---(2)...

Adding 1 and 2

<a + <b =<X +<Y

Answer 2

Answer:

join AC, then

∠CBP = ∠BCA + ∠BAC and

∠ADQ = ∠ACD + ∠DAC

(Exterior angles of triangles)

Therefore, ∠CBP + ∠ADQ = ∠BCA + ∠BAC + ∠ACD + ∠DAC

= (∠BCA + ∠ACD) + (∠BAC + ∠DAC)

= ∠C + ∠A

Hope it helps!