Anika constructed ray AC that bisected ∠A. If the m∠BAD is 46 degrees, what is 46 degrees, what is the m∠BAC

Question

A. The m∠BAC = m∠DAC.
B. The m∠BAC is 23 degrees
C. The m∠BAC is 46 degrees
D. The m∠BAC is 92 degrees

Answer 1

Given that ray AC bisects ∠A, this means that ∠BAC is equal to ∠DAC. Since we are given that m∠BAD is 46 degrees, we can conclude the following:

1. Since ∠A is comprised of angles BAD and DAC, we can express it as: m∠A = m∠BAD + m∠DAC

2. Since AC bisects ∠A, we also know that: m∠BAC = m∠DAC

3. Thus, m∠BAC = m∠DAC = x (let's say) This means: m∠BAD + m∠DAC = 46° + x = 2x

4. Therefore: 46° + x = 2x ⇒ 46° = x ⇒ m∠BAC = 23°

Thus, the correct answer is: B. The m∠BAC is 23 degrees.