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

Question

solve it and explain to me why it is that one

(1 point)
Responses

The m∠BAC is 92 degrees.
The m angle upper B upper A upper C is 92 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 23 degrees.
The m angle upper B upper A upper C is 23 degrees.

The m∠BAC is 46 degrees.

Answer 1

To solve the problem, we first need to understand the information given:

1. Anika constructed ray AC that bisects angle ∠A.
2. It is given that \( m \angle BAD = 46^\circ \).

When a ray bisects an angle, it means that it divides that angle into two equal parts.

In this case, ray AC bisects angle ∠A, which consists of two angles: ∠BAD and ∠DAC. Since ray AC bisects angle ∠A, it follows that:

\[ m \angle BAC = m \angle DAC \]

Now we can find the measure of angle ∠BAC.

We know from the problem that:

• \( m \angle BAD = 46^\circ \)

Let’s represent the measures of the angles:

• \( m \angle BAC = x \)
• \( m \angle DAC = x \)

The entire angle ∠A can then be expressed as:

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

Since AC bisects angle A and the measure of angle ∠A is made up of angles BAD and DAC, we have:

\[ m \angle BAD = m \angle DAC \]

Thus, if we calculate it:

\[ m \angle A = 46^\circ + 46^\circ = 92^\circ \]

So, the measure of angle ∠BAC is:

\[ m \angle BAC = m \angle DAC = 46^\circ \]

Therefore, the answer is:

The m∠BAC is 46 degrees.

This is the correct answer because it is based on the fact that angle AC bisects angle A into two equal angles, and since one of those angles (∠BAD) is given as 46 degrees, the other angle (∠DAC or ∠BAC) is also equal to 46 degrees.