Question

Two of the statements are true; one is a lie.

Select the one that is a lie.
Then explain your reasoning.

∠BAF and ∠CAF are complementary.
∠BAF and ∠BAC are adjacent.
∠DAC and ∠CAB are supplementary.

Answer 1

Answer: Choice B

angle BAF and angle BAC are adjacent

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Step-by-step explanation:

Let's go through each of the answer choices.

• Choice A is true since angles BAF and CAF form a right angle (90 degree angle). So we can rule this out.
• Choice B is false. This is the answer. Adjacent angles must share a common ray or side, which does happen with the two angles in question (both share ray AB); however, note that angle BAF is completely inside angle BAC. We cannot have this overlap, or any overlap at all, when it comes to adjacent angles.
• Choice C is true. The two angles combine or glue together to form a straight angle, which is 180 degrees. We can rule this answer choice out.

Answer 2

Angle BAF and angle BAC is incorrect.

They overlap: adjacent angles do not overlap.