Let the angle bac be x. Since angle acb is double of angle bac, angle acb equals 2x. Now, since angle cba is congruent angle acb, angle acb also equals 2x.
Draw the figure.
To find the angle measures, use the fact that the angle sum of a triangle is 180 degrees. So,
[tex]\begin{gathered} x+2x+2x=180 \\ 5x=180 \\ x=\frac{180}{5} \\ =36^{\circ} \end{gathered}[/tex]
The smallest angle, angle bac is 36 degrees and the other two angles angle abc and angle acb is of 72 degrees.
