Respuesta :

chloedowns1028

Answer:

The second choice is correct.

Step-by-step explanation:

    These are triangles, so the interior angles have to add up to 180 degrees. Since 45 degrees and m<1 are vertical angles, they will have the same measure. So right off the back we know that m<1 =45. To find the measure<2 all you need to do is add 45 and 59, then subtract that answer from 180. M<2= 76. That leaves only one option. The second  one.

luisejr77

Answer: Second option.

Step-by-step explanation:

You can observe in the figure that the angle 45° and the angle ∠1 share the same vertex. This means that they are "Vertical angles". Therefore, they are congruent:

 [tex]m\angle 1=45\°[/tex]

We need to remember that the sum of the interior angles of a triangle is 180 degrees. Then [tex]m\angle 2[/tex] is:

[tex]m\angle 2+59\°+45\°=180\°\\m\angle 2=180\°-59\°-45\°\\m\angle 2=76\°[/tex]

And you can apply the same procedure to find  [tex]m\angle 3[/tex]. This is:

[tex]m\angle 1+m\angle 3+55\°=180\°\\45\°+m\angle 3+55\°=180\°\\m\angle 3=180\°-55\°-45\°\\m\angle 3=80\°[/tex]

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