Question

Four Boys are playing with a ball in a circular park the position of each boy is represented by A, B,C and D ​

Answer 1

Answer:

Step-by-step explanation:

Since, the opposite angles of a cyclic

quadrilateral are supplementary.

angle A + angle C = 180°

4y – 4 + 2x + 4 = 180°

 x + 2y = 90° ...(i)

and angle B + angle D = 180°

5y + 5 + x + 10 = 180°

x + 5y = 165° ...(ii)

On solving, we get x = 40° and y = 25°

(ii) angle A = 4y – 4 [given]

Putting y = 25 from part (i), we get

angle A = 4 × 25 – 4= 96°

and angle B = 5y + 5 [given]

Putting, y = 25, we get

angle B = 5 × 25 + 5 = 130°

Similarly, angle A = 4y – 4 = 96°

[Proved above]

and angle C = 2x + 4

Putting x = 40 from part (i), we get

angle C = 2 × 40 + 4 = 84°

angle A + angle C = 96° + 84°

= 180°,         Hence prooved