Question

Find the value of x,y,z.

What is value of x,y,z.

Answer 1

X=7

Y and Z = 128

Explanation:

7X+3=4X+24

it is equal coz by the opposite angle

find the value of X

7x+3=4x+24--------------collect like term

3x=21----------divided by 3

x=7

then 7x+3=52

4x+24=52

SR is the line that measure 180°

that means (7x+3)+Z=180°

use the value of X into the equation

Z=180-52

Z=128

it means Z and Y are equal so Y= 128

Answer 2

`x=7\\y=128\\z=128`

Explanation:

Value of x:-

Form an equation:

`4x+24=7x+3` {opposite / vertical angles are equal}

Subtract 7x from both sides:

`4x+24-7x=7x+3-7x`

`-3x+24=3`

Subtract 24 from both sides:

`-3x+24-24=3-24`

`-3x=-21`

Divide both sides by -3

`-3x/-3=-21/-3`

`x=7`

Value of y and z:-

Value of x is 7 so replace x in the equations:

`4(x)+24=52\\7(7)+3=52`

Now that we have the value of x, its easy to find y and z

`52+52+y+z=360`

{complete circle makes 360°}

`104+y+z=360`

`y+z=360-104`

`y+z=256`

Divide 256 by 2 to get value of each variable:

vertically opposite angles (y & z) are equal

`256/2 = 128`

`y=128\\z=128`

∴ CHECK: 128 + 128 + 52 + 52 = 360°

hope this helps...