Answer:
[tex]\Large\boxed{m\angle 1 = 110 \textdegree}[/tex]
[tex]\Large\boxed{m\angle 2 = 70 \textdegree}[/tex]
[tex]\Large\boxed{m\angle 3 = 70 \textdegree}[/tex]
[tex]\Large\boxed{m\angle 5 = 110 \textdegree}[/tex]
[tex]\Large\boxed{m\angle 6 = 70 \textdegree}[/tex]
[tex]\Large\boxed{m\angle 7 = 70 \textdegree}[/tex]
[tex]\Large\boxed{m\angle 8 = 110 \textdegree}[/tex]
Step-by-step explanation:
We can use basic angle relationships to find the values of m∠1-8.
Let's first note that line t is being intersected by two parallel lines, L and m. This means that the angles formed by both intersections will be the same.
First off, we know that the 110° is an opposite angle to m∠1. This means their angle measures are the same, so m∠1 is 110°.
We also know that m∠1 and m∠2 are supplementary. This means their angle measures will add up to 180°. This means m∠2 is [tex]180-110=70 \textdegree[/tex].
m∠2 is also opposite to m∠3. Therefore, their angle measures are the same, and m∠3 = 70°.
Now, we can start thinking about corresponding angles. Basically - what angle formed by line L will correspond to which angle formed by line M?
We can see that m∠2 is corresponding to m∠6. Therefore, their angle lengths are the same, so m∠6 is also 70°.
Now we can use the same logic that we did for line L in line M.
m∠7 and m∠6 are opposite angles, so m∠7 is 70°.
m∠8 is supplementary to m∠6, so m∠8 is [tex]180-70=110 \textdegree[/tex].
m∠5 and m∠8 are opposite angles, so m∠5 is also 70°.
Hope this helped!
