Question

sion find the values of x and y in the trapezoid. justify your answer. (2x + 12)° (y + 44)° (3y)° 86°

Explanation:

Step1: Use property of same - side interior angles

In a trapezoid, the sum of same - side interior angles (adjacent angles along a non - parallel side) is 180°.
We have two pairs of same - side interior angles.
For the pair with angles \((y + 44)^{\circ}\) and \((3y)^{\circ}\), we set up the equation \((y + 44)+3y=180\).
Combining like terms: \(y+3y + 44=180\), which simplifies to \(4y+44 = 180\).
Subtract 44 from both sides: \(4y=180 - 44\), so \(4y=136\).
Divide both sides by 4: \(y=\frac{136}{4}=34\).

Step2: Use property of same - side interior angles for x

For the other pair of same - side interior angles \((2x + 12)^{\circ}\) and \(86^{\circ}\), we set up the equation \((2x + 12)+86=180\).
Combine like terms: \(2x+98 = 180\).
Subtract 98 from both sides: \(2x=180 - 98\), so \(2x = 82\).
Divide both sides by 2: \(x=\frac{82}{2}=41\).

Answer:

\(x = 41\), \(y = 34\)