Question

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

Answer 1

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

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 =
`(391)/(23)`

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