Question

in the given figure, if x/3 = y/4 = z/5, then calculate the values of x, y and z​

Answer 1

Answer:

the answer is 60

Step-by-step explanation:

Let x/3 y/4 z/5 = k

x = 3k

y = 4k and z = 5k

In cyclic qudarilateral ABCD, the side BC is produced to Q.

:. angle A = angle DCQ = x

(exterior angle of a cyclic quadrilateral is equal to its interior opposite angle)

Also, in ∆CDQ, the side QD is produced to A

⇒ angle ADP = x + z

( exterior angle of a triangle is equal to the sum of its two int., opposite angles)

Now, in ∆ ADP

angle A + angle ADP + angle APD = 180°

( sum of angles of a triangle is 180°)

x + (x = z) + y = 180°

⇒ 2x + y + z = 180°

⇒ 2(3k) + 4k+ 5k = 180°

⇒ 6k + 4k+ 5k = 180°

⇒15k = 180° ⇒k = 180° / 15 = 12°

x = 3k 3 x 12 = 36°

y = 4k = 4 x 12 = 48°

and z = 5k = 5 x 12 = 60°