Use the image to answer the following question.

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

The m∠BAC is 23 degrees.
The m angle upper B upper A upper C is 23 degrees.

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 92 degrees.

Answer 1

To solve for the measure of angle \( m∠BAC \), we can use the fact that ray \( AC \) bisects angle \( A \).

Given that:

• \( m∠BAD = 46^\circ \)

Since ray \( AC \) bisects \( ∠A \), we know that:

• \( m∠BAC = m∠CAD \)

Therefore, the total measure of angle \( A \) can be represented as: \[ m∠BAC + m∠CAD = m∠BAD \]

Since \( m∠BAC = m∠CAD \), we can express this as: \[ 2 \cdot m∠BAC = m∠BAD \] \[ 2 \cdot m∠BAC = 46^\circ \] \[ m∠BAC = \frac{46^\circ}{2} = 23^\circ \]

Thus, the measure of angle \( m∠BAC \) is \( 23^\circ \).

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