I'm still working on this, but angle DCE is 90. Angle BCA is 80, so the exterior is 100, so each half is 50, and so on.
ABC is an acute angled triangle. . The angle bisector of meets AB in D. Let the perpendicular bisector of side AB meet the angle bisector of in E. Join E and C. Its given that CE bisects exterior (i.e. ).
The figure i have attached is not very clear but you do not need the figure. the text i have written is sufficient to understand the question.
let the point intersecting EF and BC be M and the point intersecting ED and BC be N.
consider point D, since
from you'll find
now sum up all the angles in the quadrilateral and find x
the answer will be 20