In triangle CDE, the sides CD is equal to side CE, so angle opposite to side CD is equal to angle opposite to side CE, means
[tex]\angle CDE=\angle CED[/tex]
Determine the measure of angle CDE (or angle CED) by using angle sum property of triangle.
[tex]\begin{gathered} \angle CDE+\angle CED+\angle DCE=180 \\ \angle CDE+\angle CDE+50=180 \\ 2\angle CDE=180-50 \\ \angle CDE=\frac{130}{2} \\ \angle CDE=65 \end{gathered}[/tex]
The measure of angle CDE is 65 degrees.
The angle CDE and angle CDA are linear pair of angles. So,
[tex]\angle CDE+\angle CDA=180[/tex]
Substitute the measure of angle CDE to obtain the measure of angle CDA.
[tex]\begin{gathered} 65+\angle CDA=180 \\ \angle CDA=180-65 \\ =115 \end{gathered}[/tex]
Consider the triangle CAD.
Determine the measure of angle DCA by using angle sum property of triangle.
[tex]\begin{gathered} \angle CAD+\angle CDA+\angle DCA=180 \\ 40+115+\angle DCA=180 \\ \angle DCA=180-155 \\ =25 \end{gathered}[/tex]
So measure of angle DCA is 25 degrees.
