Question

Find each angle and tell me the angle relationship i apologize for the work ok the side

Answer 1

Consider that the given figure depicts two intersecting lines, thereby forming 4 angles.

These angles can be referred to as the upper angle (U), lower angle (L), left side angle (LS), and right side angle (RS).

According to the given information,

`\begin{gathered} \angle U=14x-22 \\ \angle L=11x+14 \\ \angle LS=2x+5y \end{gathered}`

Theorem: The vertically opposite angles formed by the intersection of two lines are always equal.

It follows that,

`\begin{gathered} \angle U=\angle L \\ 14x-22=11x+14 \\ 14x-11x=14+22 \\ 3x=36 \\ x=12 \end{gathered}`

Theorem: The sum of angles constituting a straight line is always 180 degrees.

It follows that,

`\begin{gathered} \angle U+\angle LS=180 \\ 14x-22+2x+5y=180 \\ 16x+5y=180+22 \\ 16(12)+5y=202 \\ 5y=202-192 \\ y=(10)/(5) \\ y=2 \end{gathered}`

Now that we know the values of the variables 'x' and 'y', the values of the angles can be obtained as follows,