A parallelogram has equal opposite angles and the two adjacent angles are supplementary (180 degrees).
Thus, from the figure given, we have:
(3x + 15) + (3x - 15) = 180
Let's solve for x.
Expand the parentheses:
3x + 15 + 3x - 15 = 180
Combine like terms:
3x + 3x + 15 - 15 = 180
6x + 0 = 180
6x = 180
Divide both sides by 6:
[tex]\begin{gathered} \frac{6x}{6}=\frac{180}{6} \\ \\ x=30 \end{gathered}[/tex]
To find y, we have the equation:
(3x - 15) = y + 30
Since x is 30, substitute 30 for x and solve for y.
3(30) - 15 = y + 30
90 - 15 = y + 30
75 = y + 30
Subtract 30 from both sides:
75 - 30 = y + 30 - 30
45 = y
y = 45
ANSWER:
x = 30 ; y = 45
