Use a definition, postulate, or theorem to find the value of x in the figure described.


< means angle

The value of x is 47

Step-by-step explanation:

* Lets explain the meaning of linear pair of angles

- A linear pair of angles is formed when two lines intersect

- If two angles are adjacent angles formed by two intersecting lines,

then the two angles are a linear pair of angles

- The measure of a straight angle is 180°, then the measure of the

linear pair of angles is 180°

- That means the sum of the measures of the two angles is 180°

* Lets solve the problem

∵ ∠ABC and ∠CBD are a linear pair angles

∴ m∠ABC + m∠CBD = 180°

- The measures of the two angles are equal

∵ m∠ABC = m∠CBD = (2x - 4) °

- To find the value of x equate the sum of them by 180

∴ (2x - 4) + (2x - 4) = 180

- Collect like terms in the left hand side

∵ (2x + 2x) + (-4 + - 4) = 180

∴ 4x + - 8 = 180

- Remember (+) (-) = (-)

∴ 4x - 8 = 180

- Add 8 to both sides

∴ 4x = 188

- Divide both sides by 4

∴ x = 47

∴ The value of x is 47