Answer:
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