What is m<3? Thank you

Explanation:

Let

The goal is to find y

For now, focus on the interior angles of triangle DEF. We have these three angles:

Those interior three angles add to 180. This is true for any triangle.

D+E+F = 180

90+53+x = 180

143+x = 180

x = 180-143

x = 37

angle 2 = 37 degrees

Now we can find y.

Focus on angles 2 and 3, which are x and y respectively. These two angles add to 180 because they form a straight line. Note: the triangle's angles summing to 180 is closely related to this idea where angle 2 and angle 3 are a linear pair.

So this means,

(angle2)+(angle3) = 180

x+y = 180

37+y = 180

y = 180-37

y = 143

angle 3 = 143 degrees

It's not a coincidence that we ended up with a previously calculated value of 143. It turns out that adding the remote interior angles D and E leads to the exterior angle EFG.

D+E = 90+53 = 143 = angle EFG

I'm using the remote interior angle theorem. Some textbooks may call this the exterior angle theorem. In my opinion, the phrasing "remote interior angle theorem" is more descriptive.

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