Question

X =x=x, equals
^\circ
∘

Answer 1

Answer:
`55^(\circ)`

Explanation:

Angles on a straight line add to
`180^(\circ)`.

Answer 2

Given that the sum of all angles around a point is
`$360^(\circ)$`, we sum the known angles and subtract from
`$360^(\circ)$` to find
`$x$` :

`$$360^(\circ)-\left(125^(\circ)+35^(\circ)+180^(\circ)\right)=360^(\circ)-340^(\circ)=20^(\circ)$$`

To solve for
`$x$` in the given diagram of angles, we need to apply the properties of angles formed by intersecting lines. Here's a step-by-step calculation:

1. Identify Relationships: The diagram shows angles formed by intersecting lines, so we can use the fact that the sum of angles around a point is
`$360^(\circ)$`.

2. Set Up Equation: If we add all the angles around the intersection point, including
`$x$`, we should get
`$360^(\circ)$`. So the equation will be:

`$$125^(\circ)+x^(\circ)+35^(\circ)+\left(180^(\circ)-x^(\circ)\right)=360^(\circ)$$`

Note that the angle directly opposite to
`$x$` must be
`$180^(\circ)-x^(\circ)$` because they form a straight line which sums up to
`$180^(\circ)$`.

3. Solve for
`$x$` :

`$$\begin{aligned}& 125^(\circ)+x^(\circ)+35^(\circ)+180^(\circ)-x^(\circ)=360^(\circ) \\& x^(\circ)-x^(\circ)+125^(\circ)+35^(\circ)+180^(\circ)=360^(\circ) \\& 125^(\circ)+35^(\circ)+180^(\circ)=360^(\circ) \\& 340^(\circ)=360^(\circ)\end{aligned}$$`

This simplifies the equation, and we can now solve for
`$x$` by subtracting the sum of known angles from
`$360^(\circ)$`.

4. Calculation: Let's do the calculation.

The value of
`$x$` is
`$20^(\circ)$`.