Question

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.

Answer 1

Statement 3

Explanation:

∠GAF ≅ ∠TAE

Since, there is no relation between these angles,

Therefore, statement is False.

∠TAE and ∠FAH are complementary.

If the sum of the two angles is 90°, pair of angles is said to be complimentary angles.

Therefore, this statement is False.

∠TAF is obtuse.

Measure of obtuse angle is more than 90°

From the given picture, measure of ∠TAF = m∠TAH + m∠HAF

= 90° + 50°

= 140°

Here, m∠TAF > 90°

Therefore, ∠TAF is an obtuse angle.

Statement (3) is the correct statement.