Question

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

Explanation:

Step1: Recall parallelogram angle property

In a parallelogram, opposite angles are equal. So, we set the two given angle expressions equal:
$$6n - 70 = 2n + 10$$

Step2: Solve for \( n \)

Subtract \( 2n \) from both sides:
$$6n - 2n - 70 = 10$$
$$4n - 70 = 10$$

Add 70 to both sides:
$$4n = 10 + 70$$
$$4n = 80$$

Divide by 4:
$$n = \frac{80}{4} = 20$$

Step3: Find the angle measure

Substitute \( n = 20 \) into one of the angle expressions (e.g., \( 2n + 10 \)):
$$2(20) + 10 = 40 + 10 = 50^\circ$$

Adjacent angles in a parallelogram are supplementary (sum to \( 180^\circ \)), so the other angle is:
$$180^\circ - 50^\circ = 130^\circ$$

Answer:

50° and 130° (corresponding to the option "50° and 130°")