Question

Use the image to answer the following question.

A triangle has vertices labeled upper A, upper B, and upper D. A point on the line segment formed between points upper B and upper D is labeled upper C . A line connects points upper A and upper C, and a ray extends rightward from this line.

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

(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 23 degrees.
The m angle upper B upper A upper C is 23 degrees.

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

The m∠BAC
is 92 degrees.

Answer 1

Since ray AC bisects ∠A, we know that ∠BAC is equal to ∠DAC.

Given that m∠BAD is 46 degrees, we can express ∠A as the sum of ∠BAC and ∠DAC. Since AC bisects ∠A, we know that:

m∠A = m∠BAC + m∠DAC
m∠A = 46 degrees

Because ∠BAC = ∠DAC, we can set them both equal to x:

m∠A = x + x = 2x

Now we can set this equal to the measure we found:

2x = 46

Now, divide both sides by 2 to find x:

x = 23 degrees

Thus, m∠BAC = 23 degrees.

The correct response is: **The m∠BAC is 23 degrees.**