Two of the statements are true; one is a lie. Select the one that is a lie.
Then explain your reasoning.

∠GAF ≌ ∠TAE.
∠TAE and ∠FAH are complementary.
∠TAF is obtuse.

Choice A

angle GAF = angle TAE is the lie (aka false statement)

Explanation:

Let's go through each answer choice to see which is true or which is false.

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.

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.

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.

lo.lll

step-by-step explanation: