Question

Determine the values of x and y for the parallelogram (3x+15)° (Y+30)° (3x-15)°

Answer 1

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:

`\begin{gathered} (6x)/(6)=(180)/(6) \\ \\ x=30 \end{gathered}`

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