Question

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