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

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28-10-2022
Mathematics

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

Answer :

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SerasJ752119 SerasJ752119 · Answer 1 · 2022-10-28T15:59:42-04:00

According to the problem,

[tex]\begin{gathered} m\angle8=23 \\ \end{gathered}[/tex]

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

[tex]m\angle8=m\angle6=23[/tex]

Since they are vertical angles.

Then, we have.

[tex]m\angle6=m\angle4=23[/tex]

By alternate interior angles.

Also,

[tex]\begin{gathered} m\angle4+m\angle5=180 \\ 23+m\angle5=180 \\ m\angle5=180-23 \\ m\angle5=157 \end{gathered}[/tex]

By same-side interior angles.

Then,

[tex]m\angle7=m\angle5=157[/tex]

By vertical angles.

Additionally,

[tex]m\angle3=m\angle7=157[/tex]

By corresponding angles.

Now, we have.

[tex]\begin{gathered} m\angle1=m\angle5=157 \\ m\angle2=m\angle6=23 \end{gathered}[/tex]

By corresponding angles.

Therefore, the missing angles are:

[tex]\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}[/tex]

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

Answer :

Therefore, the missing angles are:

Other Questions

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