The below figure is a parallelogram. Find the values for each variable.
Accepted Solution
A:
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 ParallelogramConsecutive angles of parallelogram are supplementarySo, 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° ........1And ( 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° .........2Now, from eq 1 and eq 2 7 y + 3 x = 185° 3 × ( 10 y + x ) = 192° × 3Or, 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 xI.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