Question

jacob is cutting a tile in the shape of a parallelogram. two opposite angles have measures of (6n - 70)° and (2n + 10)°. what are the two different angle measures of the parallelogram - shaped tile? 20° and 160° 50° and 130° 30° and 150° 70° and 110°

Explanation:

Step1: Use the property of parallelogram (opposite angles are equal)

Since opposite angles of a parallelogram are equal, we set \(6n - 70=2n + 10\).

Step2: Solve the equation for \(n\)

Subtract \(2n\) from both sides: \(6n-2n - 70=2n-2n + 10\), which gives \(4n-70 = 10\).
Add \(70\) to both sides: \(4n-70 + 70=10 + 70\), so \(4n=80\).
Divide both sides by \(4\): \(n=\frac{80}{4}=20\).

Step3: Find the measure of one pair of opposite angles

Substitute \(n = 20\) into \(2n + 10\): \(2\times20+10=40 + 10=50^{\circ}\).

Step4: Find the measure of the other pair of opposite angles

Since consecutive angles of a parallelogram are supplementary (sum to \(180^{\circ}\)), the other angle is \(180 - 50=130^{\circ}\).

Answer:

\(50^{\circ}\) and \(130^{\circ}\) (the second option)