We know that the exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles. In this case this means that:
[tex]7x-19=2x-1+x+10[/tex]
Solving for x we have:
[tex]\begin{gathered} 7x-19=2x-1+x+10 \\ 7x-19=3x+9 \\ 7x-3x=19+9 \\ 4x=28 \\ x=\frac{28}{4} \\ x=7 \end{gathered}[/tex]
Once we know the value of x we pluf it in the expression for the angle we want:
[tex]7\cdot7-10=49-10=30[/tex]
Therefore, the angle CDE is 30°.
