The below figure is a parallelogram. find the values for each variable.

The value of x is  22°  and The value of y is  17°  

Step-by-step explanation:

Given figure of parallelogram as show :

Let ∠ A = ( 3 y - 12 )°

    ∠ B = ( 7 y + x )°

And ∠ C = ( 2 x - 5 )°

Now From The property of Parallelogram

Consecutive angles of parallelogram are supplementary

So, from property

∠ A +  ∠ B = 180°    and   ∠ B +  ∠ C = 180°

∴ ( 3 y - 12 )° + ( 7 y + x )° = 180°

Or, ( 3 y + 7 y )° + ( x - 12 )° =  180°

Or, 10 y + x = 180° + 12°

I.e  10 y + x = 192°                              ........1

And ( 7 y + x )° + ( 2 x - 5 )° = 180°

Or, ( 7 y - 5 )° + ( x + 2 x )° =  180°

Or,  7 y + 3 x =  180° + 5°

I.e  7 y + 3 x =  185°                            .........2

Now, from eq 1 and eq 2

  7 y + 3 x =  185°      

 3 × ( 10 y + x ) = 192° × 3

Or, 30 y + 3 x = 576°

So, (  30 y + 3 x ) - ( 7 y + 3 x ) =  576° - 185°

or,  ( 30 y - 7 y ) + ( 3 x - 3 x ) = 391°

so,  23 y = 391°

∴   y =

I.e y = 17°

Put The value of y in eq 1 to get the value of x

I.e  10 y + x = 192°    

or,  10 × 17 + x = 192°  

Or, x = 192° - 170°

I.e x = 22°

Hence The value of x is  22°  and The value of y is  17°   Answer

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls