DeltaMath Inter and Exterior Triangle angles

Question

In ΔBCD,  BD is extended through point D to point E,  m∠BCD=(2x−1)∘,  m∠CDE=(7x−19)∘,   and m∠DBC=(x+10)∘.   Find m∠CDE.

Answer 1

The measure of the exterior angle CDE (7x - 19) equals the sum of the measures of the two non-adjacent interior angles DBC (x + 10) and BCD (2x - 1) so:

x + 10 + 2x - 1 = 7x - 19

3x + 9 = 7x - 19

28 = 4x

7 = x

substituting into the value for CDE (7x - 19); 7(7) - 19 = 30