Question

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

(1 point)
Responses

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

The m∠BAC
is 92 degrees.

Answer 1

To find \( m\angle BAC \) given that ray \( AC \) bisects \( \angle A \) and \( m\angle BAD = 46^\circ \), we can use the definition of an angle bisector.

Since ray \( AC \) bisects \( \angle A \), it means that:
\[
m\angle BAC = m\angle DAC
\]

Let \( m\angle BAC = x \). Since \( \angle BAD \) is composed of \( \angle BAC \) and \( \angle DAC \), we can set up the equation:
\[
m\angle BAD = m\angle BAC + m\angle DAC
\]
\[
46^\circ = x + x
\]
\[
46^\circ = 2x
\]

Solving for \( x \):
\[
x = \frac{46^\circ}{2} = 23^\circ
\]

Therefore, \( m\angle BAC \) is \( 23^\circ \).

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