Question

What is the value of x?

Answer 1

x = 34.5

Explanation:

According to the Vertical Angles Theorem, when two straight lines intersect, the opposite vertical angles are congruent.

Therefore, the vertical angle opposite the angle labelled 40° is also 40°.

Assuming lines m and n are parallel, we can apply the Same-side Interior Angles Theorem to find the value of x.

According to the Same-side Interior Angles Theorem, when two parallel lines are intersected by a transversal, the angles that are interior to the parallel lines and on the same side of the transversal line sum to 180°.

Therefore, the angle labelled (4x + 2)° and the angle vertically opposite to the one labelled 40° sum to 180°:

`(4x + 2)^(\circ) + 40^(\circ) = 180^(\circ)`

Solve for x:

`4x + 2 + 40 = 180`

`4x + 42 = 180`

`4x + 42-42 = 180-42`

`4x =138`

`(4x)/(4)=(138)/(4)`

`x=34.5`

Therefore, the value of x is 34.5.