Question

K

(
28) cm
V
1 cm
M
Han
56x-5
1.5 cm
W
Given that figure JKLMNWWXYZ. Find the value of y

Answer 1

`\boxed{\sf y = 6 \ cm}`

`\boxed{\sf x = 25 \degree}`

Explanation:

It is given that JKLMN
`\sim` VWXYZ

So, from this we can say that:

JK
`\sim` VW & ∠LMN
`\sim` ∠XYZ

i.e.

(2y - 8) cm = 4 cm & 4x° = 5(x - 5)°

Solving for y:

⇒2y - 8 = 4

Adding 8 to both sides:

⇒2y - 8 + 8 = 4 + 8

-8 + 8 = 0:

⇒2y = 4 + 8

4 + 8 = 12:

⇒2y = 12

Dividing both sides by 2:

⇒
`\sf (2y)/(2) = (12)/(2)`

`\sf (2)/(2) = 1:`

⇒y =
`\sf (12)/(2)`

`\sf (12)/(2) = 6:`

⇒y = 6 cm

Solving for x:

⇒4x° = 5(x - 5)°

Expanding right hand ride expression:

⇒4x° = 5x° - 25°

Adding 25° to both sides:

⇒4x° + 25° = 5x° - 25° + 25°

25° - 25° = 0°:

⇒4x° + 25° = 5x°

⇒5x° = 4x° + 25°

Substracting 4x° from both sides:

⇒5x° - 4x° = 4x° - 4x° + 25°

4x° - 4x° = 0°:

⇒5x° - 4x° = 25°

5x° - 4x° = x°:

⇒x° = 25°