Question

if angle 8 equals 23 degrees find the measure of each missing angle give your reasoning*Don't forget to give the reasoning.*

Answer 1

According to the problem,

`\begin{gathered} m\angle8=23 \\ \end{gathered}`

We have one pair of parallel lines and one transversal line.

Since those lines are parallel all 8 angles are related someway.

In the given graph, we have vertical angles, corresponding angle, alternate interior angles, alternate exterior angles, supplementary angles.

We know that

`m\angle8=m\angle6=23`

Since they are vertical angles.

Then, we have.

`m\angle6=m\angle4=23`

By alternate interior angles.

Also,

`\begin{gathered} m\angle4+m\angle5=180 \\ 23+m\angle5=180 \\ m\angle5=180-23 \\ m\angle5=157 \end{gathered}`

By same-side interior angles.

Then,

`m\angle7=m\angle5=157`

By vertical angles.

Additionally,

`m\angle3=m\angle7=157`

By corresponding angles.

Now, we have.

`\begin{gathered} m\angle1=m\angle5=157 \\ m\angle2=m\angle6=23 \end{gathered}`

By corresponding angles.

Therefore, the missing angles are:

`\begin{gathered} m\angle1=157,\text{ by corresponding angles.} \\ m\angle2=23,\text{ by corresponding angles.} \\ m\angle3=157,\text{ by corresponding angles.} \\ m\angle4=23,\text{ by alternate interior angles.} \\ m\angle5=157,\text{ by same-side interior angles.} \\ m\angle6=23,by\text{ vertical angles.} \\ m\angle7=157\text{, by vertical angles.} \\ m\angle8=23,\text{ by given.} \end{gathered}`