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°.

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