Answer:
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 = [tex]\frac{391}{23}[/tex]
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
