Question

The sides BA and DC of a quadrilateral are produced as shown in the figure given figure prove that X + Y is equal to a + b

Answer 1

where is the figure?

Answer 2

SOLUTIONS:

We have ∠A + b° = 180° [Linear Pair]

→ ∠A = (180° - b°) .......(i)

Also, ∠C + a° = 180° [Linear Pair]

→ ∠C = (180° - a°) .......(ii)

Now, ∠A + ∠B + ∠C + ∠D = 360° [Sum of the ∠s of a quadrilateral is 360°]

→ (180° - b°)+ x° + (180° - a°)+ y° = 360° [Using (i) and (ii)]

→ x + y = a + b