Answer: Choice A
angle GAF = angle TAE is the lie (aka false statement)
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Step-by-step explanation:
Let's go through each answer choice to see which is true or which is false.
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Choice A
The markers for angles GAF and TAE are different. Both would need to have a single angle marker, or a double angle marker. The differing markers indicates the angles aren't the same.
Also, note that angle TAG isn't a 180 degree angle, or that point G isn't on line TA. We need this to be the the case, so that two vertical angles form. However, such a thing doesn't happen.
So that's why angles TAE and GAF aren't the same measure.
Choice A is the answer. You can stop here if you wanted.
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Choice B
Let
x = measure of angle TAE
y = measure of angle TAH
z = measure of angle HAF
We can see that x+y+z = 180, since angle EAF is a straight angle. The diagram gives y = 90 and z = 50, so,
x+y+z = 180
x+90+50 = 180
x+140 = 180
x = 180-140
x = 40
Angle TAE is 40 degrees. It adds with angle FAH to get 40+50 = 90, showing that the two angles are indeed complementary.
Choice B is a true statement, so we can rule it out.
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Choice C
Angle TAF is composed of angles TAH and HAF
Adding the two angles gets us 90+50 = 140, which is larger than 90.
Therefore angle TAF is obtuse.
Choice C is a true statement, and it can be ruled out as well.
Technically you could have stopped at choice A once you found the lie, but I figured to show why choices B and C could be ruled out.