Which reason completes the proof in the picture A.alternate interior angles converse
B.opposite sides of a parallelogram are congruent
C.opposite angles of a parallelogram are congruent
D.alternate interior angles theorem

The error the student made is referring to an angle, m<1, being equal to 80 degrees. It is incorrect to assign a measurement or value to an angle without any given information or reference point.

the smaller number is 8, and the larger number is 12, and they indeed add up to 20, and three times the smaller number (3 * 8) is equal to two times the larger number (2 * 12).

Let's call the two numbers x and y, with x being the smaller number and y being the larger number.

We have two pieces of information from the problem:

1. The sum of the two numbers is twenty:

  x + y = 20

2. Three times the smaller number is equal to two times the larger number:

  3x = 2y

Now, we can solve this system of linear equations.

First, we can solve equation (1) for x:

x = 20 - y

Now, substitute this expression for x into equation (2):

3(20 - y) = 2y

Now, distribute the 3 on the left side:

60 - 3y = 2y

Now, isolate the variables on one side of the equation and constants on the other side:

60 = 2y + 3y

Combine like terms:

60 = 5y

Now, divide by 5 to solve for y:

y = 60 / 5

y = 12

Now that we have found the value of y, we can substitute it back into equation (1) to find x:

x + 12 = 20

Subtract 12 from both sides:

x = 20 - 12

x = 8

So, the two numbers are:

x = 8 (smaller number)

y = 12 (larger number)

Therefore, the smaller number is 8, and the larger number is 12, and they indeed add up to 20, and three times the smaller number (3 * 8) is equal to two times the larger number (2 * 12).

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Answer:

The smaller number is 8

The larger number is 12

Step-by-step explanation:

Let the smaller number be x

Let the larger number be y

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