Answer: 143 degrees
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Step-by-step explanation:
Let
- x = the measure of angle 2
- y = the measure of angle 3
The goal is to find y
For now, focus on the interior angles of triangle DEF. We have these three angles:
- D = 90 (due to the square angle marker)
- E = angle 1 = 53
- F = angle 2 = x
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.