Question

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

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

The m∠BAC
is 23 degrees.

Answer 1

Since ray AC bisects ∠A, we know that the two angles formed by the bisection are equal.

Given that \( m∠BAD = 46^\circ \), we can denote:

- \( m∠BAC \) = \( x \)
- \( m∠DAC \) = \( x \)

Since \( \angle A \) is made up of \( \angle BAD \) and \( \angle DAC \), we can write:

\[
m∠A = m∠BAD + m∠DAC = 46^\circ + x
\]

Since ray AC bisects angle \( A \), we have:

\[
m∠BAC = m∠DAC = x
\]

Thus, we can set up the equation:

\[
x + x = 46^\circ
\]

So,

\[
2x = 46^\circ
\]

Dividing by 2 gives:

\[
x = 23^\circ
\]

Therefore,

\[
m∠BAC = 23^\circ
\]

The correct response is:

**The m∠BAC is 23 degrees.**