Ines examined the triangle and noticed that segment AD

bisected ∠CAB
. She measured ∠BAD
to be 21 degrees. What is the measure of ∠CAB
in degrees?

(1 point)
The m∠CAB
is
degrees.

1 answer

Since segment \( AD \) bisects angle \( CAB \), we know that:

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

Because \( AD \) is the angle bisector, \( m\angle BAD = m\angle DAC \). Let’s denote \( m\angle BAD \) as \( x \). Therefore,

\[ m\angle CAB = x + x = 2x \]

Given that \( m\angle BAD = 21^\circ \), we have:

\[ x = 21^\circ \]

Thus:

\[ m\angle CAB = 2x = 2 \times 21^\circ = 42^\circ \]

Therefore, the measure of \( \angle CAB \) is \( \mathbf{42} \) degrees.