Question

Jacob is cutting a tile in the shape of a parallelogram. Two opposite angles have measures of (6 - 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°

Answer 1

50° and 130°

Explanation:

Here are the steps to find the two different angle measures of the parallelogram-shaped tile:

Step 1:

• Since opposite angles in a parallelogram are congruent, we can set the expressions for the two opposite angles equal to each other:

(6n - 70 = 2n + 10) - 2n

(4n - 70 = 10) + 70

(4n = 80) / 4

n = 20

Thus, n = 20

Step 2:

• We can substitute 20 for n in 6n - 70 and 2n + 10 to find their respective angle measures:

Substituting 20 for n in 6n - 70:

6(20) - 70

120 - 70

50

Substituting 20 for n in 2n + 10:

2(20) + 10

40 + 10

50

So, the two different angle measures of the parallelogram-shaped tile are 50 degrees and 130 degrees (since the sum of two opposite angles in a parallelogram is 180 degrees).

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