The angle measurements in the diagram are represented by the following expressions.

Given:

To find:

The value of x and measure of angle B

Solution:

Alternate interior angle theorem:

If two parallel lines cut by a transversal, then the alternate interior angles are congruent.

⇒ m∠A = m∠B

Add 12° on both sides.

Subtract 2x from both sides.

Divide by 3 on both sides.

⇒ x = 12°

Substitute x = 12° in ∠B.

m∠B = 2x + 24°

        = 2(12°) + 24°

        = 24° + 24°

        = 48°

The measure of ∠B is 48°.

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation:

7

step-by-step explanation: