Given: m∠JAK = 123°

If ∠JAM and ∠JAK are supplementary angles, then what is the measure of ∠KAL?
A.
57°
B.
60°
C.
33°
D.
55°

1 answer

Supplementary angles are two angles whose measures add up to 180 degrees. Given that \( m∠JAK = 123° \) and that \( ∠JAM \) and \( ∠JAK \) are supplementary, we can set up the equation:

\[ m∠JAM + m∠JAK = 180° \]

Substituting the value of \( m∠JAK \):

\[ m∠JAM + 123° = 180° \]

To find \( m∠JAM \), we subtract 123° from both sides:

\[ m∠JAM = 180° - 123° = 57° \]

Now, since \( ∠JAK \) and \( ∠KAL \) are adjacent angles, their measures add up to \( m∠JAK \):

\[ m∠JAK = m∠JAM + m∠KAL \]

Substituting the known values:

\[ 123° = 57° + m∠KAL \]

To find \( m∠KAL \), we subtract \( 57° \) from \( 123° \):

\[ m∠KAL = 123° - 57° = 66° \]

Since this value does not match any options and we realized the correct approach is simply to find \( m∠KAL \) directly due to \( ∠KAL \) being the remaining angle to complete \( 180^\circ\).

Since \( 180° - 123° = 57° \),

The measure of \( ∠KAL \) that should complement \( 123° \) is \( 57°\). Thus we find that: \[ \text{So the final answer is } m∠KAL = 57° \]

The correct answer is: A. 57°