Anika constructed ray AC that bisected ∠A . If the m∠BAD is 46 degrees, what is the m∠BAC ? which is the true correct answer solve it and tell me why

Question

(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 need to understand what it means for ray AC to bisect angle A.

Given:

• Ray AC bisects ∠A
• m∠BAD = 46 degrees

Since ray AC bisects ∠A, this means that it divides ∠A into two equal parts:

\[ m∠BAC = m∠DAC \]

Now, let's denote the measures of the angles:

\[ m∠BAC = x \]

Since ray AC bisects ∠A, then:

\[ m∠DAC = x \]

The total measure of angle A is the sum of these two angles:

\[ m∠A = m∠BAC + m∠DAC = x + x = 2x \]

We know that the measure of one part, m∠BAD, is 46 degrees. In this scenario, it's not given that m∠BAD is equal to m∠BAC, but rather that angle B refers to angle A's composition. We can set up an equation to relate what we know about angles A and B.

Since m∠BAD + m∠DAC = m∠A:

\[ m∠BAD + m∠BAC = 2x \]

Given that m∠BAD = 46 degrees, we can state:

\[ 46 + x = 2x \]

Rearranging gives us:

\[ 46 = 2x - x \] \[ x = 46 \]

This means:

\[ m∠BAC = 46 \text{ degrees} \]

Thus, the correct answer is:

The m∠BAC is 46 degrees.