Answer:
66°
Step-by-step explanation:
The applicable angle relations are ...
- An exterior angle of a triangle is equal to the sum of the remote interior angles.
- Vertical angles are congruent.
__
We recognize that angle HIJ, marked 105°, is an exterior angle to triangle DIJ. We also recognize that the angle marked x° is a vertical angle to angle DJI in triangle DIJ. Angles JDI, marked 39°, and DJI are remote interior angles with respect to angle HIJ.
We can use the relations described above to say that ...
∠HIJ = 39° +∠DJI
39° +x° = 105°
x° = 66° . . . . . . . subtract 39°
The measure of angle x is 66°.
