Jacob is cutting a tile in the shape of a parallelogram. Two opposite angles have measures of [tex]$(6n - 70)^{\circ}$[/tex] and [tex]$(2n + 10)^{\circ}$[/tex].

What are the two different angle measures of the parallelogram-shaped tile?

A. [tex]20^{\circ}[/tex] and [tex]160^{\circ}[/tex]

B. [tex]50^{\circ}[/tex] and [tex]130^{\circ}[/tex]

C. [tex]30^{\circ}[/tex] and [tex]150^{\circ}[/tex]

D. [tex]70^{\circ}[/tex] and [tex]110^{\circ}[/tex]

To solve for the measures of the two different angles in the parallelogram-shaped tile, let's go step by step.

1. Set the given angles equal to each other:
We know that opposite angles in a parallelogram are equal. Therefore, we can write the equation:
[tex]\[ 6n - 70 = 2n + 10 \][/tex]

2. Solve for [tex]$ n $[/tex]:
First, let's isolate [tex]$ n $[/tex] on one side of the equation. Subtract [tex]$ 2n $[/tex] from both sides:
[tex]\[ 6n - 2n - 70 = 2n - 2n + 10 \][/tex]
Simplify the equation:
[tex]\[ 4n - 70 = 10 \][/tex]
Next, add 70 to both sides to isolate the term with [tex]$ n $[/tex]:
[tex]\[ 4n - 70 + 70 = 10 + 70 \][/tex]
Simplify:
[tex]\[ 4n = 80 \][/tex]
Finally, divide both sides by 4:
[tex]\[ n = 20 \][/tex]

3. Calculate each angle:
- For the first angle:
[tex]\[ 6n - 70 = 6(20) - 70 = 120 - 70 = 50^\circ \][/tex]
- For the second angle:
[tex]\[ 2n + 10 = 2(20) + 10 = 40 + 10 = 50^\circ \][/tex]

Thus, the opposite angles we calculated (using [tex]$ n = 20 $[/tex]) are [tex]$ 50^\circ $[/tex].

4. Calculate the supplementary angles:
Since the opposite angles are equal, and the sum of angles around a point in a parallelogram is [tex]$ 360^\circ $[/tex], we have:
[tex]\[ \text{One pair of supplementary angles} = 180^\circ - 50^\circ = 130^\circ \][/tex]

Thus, the other pair of angles (which are also opposite to each other) are [tex]$ 130^\circ $[/tex].

Therefore, the two different angle measures of the parallelogram-shaped tile are:
[tex]\[ 50^\circ \text{ and } 130^\circ \][/tex]

So the correct answer is:
b) [tex]$ 50^\circ \text{ and } 130^\circ $[/tex]

wegnerkolmp2741o wegnerkolmp2741o · Answer 2 · 2024-07-01T14:25:03-04:00

Answer:

B. 50 and 130

Step-by-step explanation:

The opposite angles of a parallelogram are equal.

Setting the two values equal:

6n-70 = 2n+10

Subtract 2n from each side:

6n-2n-70 = 2n-2m+10

4n-70 = 10

Add 70 to each side:

4n = 80

Divide by 4:

4n/4 = 80/4

n = 20

We want to find the values of the angles.

The angle we are given is

2n+10 = 2(20)+10 = 40+10 = 50

The consecutive angle are supplementary, or adds to 180.

180-50 = 130

The two angles are 50 and 130 degrees.