Which angles are opposite to AC and BC? Which one has a greater measure?
BC, see solution.
Practice makes perfect
Let's start with copying the triangle with the angle measures from the given diagram.
In order to determine which side, AC or BC, is longer, we are going to use the following theorem.
If one angle of a triangle has
a greater measure than another angle,
then the side opposite to the greater angle is
longer than the side opposite to the lesser angle.
In △ ABC, AC is opposite to the angle ∠ ABC and BC is opposite to ∠ BAC. Angle ∠ ABC measures 44^(∘), while ∠ BAC measures 64^(∘). The last measure is greater than the first one.
44^(∘) = m∠ ABC < m∠ BAC=64^(∘)
Therefore, by the theorem side BC is longer than AC.
AC< BC
