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

Question

(1 point)
Responses

The m∠BAC=m∠DAC.
The m angle upper B upper A upper C equals m angle upper D upper A upper C .

The m∠BAC is 46 degrees.
The m angle upper B upper A upper C is 46 degrees.

The m∠BAC is 92 degrees.
The m angle upper B upper A upper C is 92 degrees.

The m∠BAC is 23 degrees.

Answer 1

If Ray AC bisects ∠A, it means that ∠BAC is equal to ∠DAC.

Given that m∠BAD = 46 degrees, we can express ∠A as:

m∠A = m∠BAD + m∠DAC

Since AC bisects ∠A, we can say:

m∠BAC = m∠DAC

Let m∠BAC = x. Thus, we have:

m∠BAD + m∠DAC = 46 + x = 2x

Setting these equal, we get:

46 + x = 2x

Solving this equation:

46 = x

Therefore,

m∠BAC = 46 degrees.

So, the correct response is:

The m∠BAC is 46 degrees.