Final answer:
To find the angle measures of the parallelogram, we set the expressions for opposite angles equal to each other, solve for 'n', and then determine the angle measures, which are 50° and 130° respectively.
Step-by-step explanation:
The students wants to find the two different angle measures of a parallelogram-shaped tile where two opposite angles are given by the equations (6n − 70)° and (2n + 10)°. Since opposite angles in a parallelogram are equal, we can set these two expressions equal to each other to find the value of 'n':
6n − 70 = 2n + 10
Solving for 'n', we get:
4n = 80
n = 20
Now, we'll plug the value of 'n' back into the expressions to get the angle measures:
6n − 70 = 6(20) − 70 = 120 − 70 = 50°
2n + 10 = 2(20) + 10 = 40 + 10 = 50°
Since opposite angles are equal in a parallelogram, the other two angles must also add up to 180°. Therefore, the other two angles are 180° - 50° = 130°. The angles of the parallelogram are 50° and 130°.