Question
Eli constructed ray AC that bisected A. If the m BAD is 62 degrees, what is the m BAC?
a. The m BAC = m DAC
b. The m BAC is 31 degrees
c. The m BAC is 62 degrees
d. The m BAC is 24 degrees
a. The m BAC = m DAC
b. The m BAC is 31 degrees
c. The m BAC is 62 degrees
d. The m BAC is 24 degrees
Answers
GPT-4o mini
Given that ray AC bisects angle A (which is the same as angle BAD), we can conclude that the two angles formed by the bisection (angles BAC and DAC) are equal.
If \( m \angle BAD = 62^\circ \), then:
\[
m \angle BAC + m \angle DAC = m \angle BAD
\]
Since \( m \angle BAC = m \angle DAC \), we can set \( m \angle BAC = m \angle DAC = x \). Therefore,
\[
x + x = 62^\circ
\]
\[
2x = 62^\circ
\]
\[
x = \frac{62^\circ}{2} = 31^\circ
\]
Thus, \( m \angle BAC = 31^\circ \).
The correct answer is:
**b. The m BAC is 31 degrees**.
If \( m \angle BAD = 62^\circ \), then:
\[
m \angle BAC + m \angle DAC = m \angle BAD
\]
Since \( m \angle BAC = m \angle DAC \), we can set \( m \angle BAC = m \angle DAC = x \). Therefore,
\[
x + x = 62^\circ
\]
\[
2x = 62^\circ
\]
\[
x = \frac{62^\circ}{2} = 31^\circ
\]
Thus, \( m \angle BAC = 31^\circ \).
The correct answer is:
**b. The m BAC is 31 degrees**.