Question
Ines examined the triangle and noticed that segment AD bisected CAB. She measured BAD to be 21 degrees. What is the measure of LC AB in degrees?
Answers
Answered by
GPT-4o mini
In triangle \( \triangle ABC \), if segment \( AD \) bisects angle \( CAB \) and you have that \( \angle BAD = 21^\circ \), then by the properties of angle bisectors, we know that:
\[
\angle CAD = \angle BAD
\]
Since \( AD \) is an angle bisector, we can state that:
\[
\angle CAD = 21^\circ
\]
Now, to find the measure of angle \( CAB \) (which is the entire angle), we simply add the two equal angles together:
\[
\angle CAB = \angle BAD + \angle CAD = 21^\circ + 21^\circ = 42^\circ
\]
Thus, the measure of angle \( CAB \) is \( 42^\circ \). Therefore, \( \angle CAB = 42^\circ \).
\[
\angle CAD = \angle BAD
\]
Since \( AD \) is an angle bisector, we can state that:
\[
\angle CAD = 21^\circ
\]
Now, to find the measure of angle \( CAB \) (which is the entire angle), we simply add the two equal angles together:
\[
\angle CAB = \angle BAD + \angle CAD = 21^\circ + 21^\circ = 42^\circ
\]
Thus, the measure of angle \( CAB \) is \( 42^\circ \). Therefore, \( \angle CAB = 42^\circ \).
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