Answer:
x = 104°
Step-by-step explanation:
The 142° and <DCE form a straight line, and a straight line measures 180°, do the two angles add up to it:
180° = 142° + m<DCE
m<DCE = 38°
The red symbol in <DCE and <CDE mean they are congruent, so m<CDE is the same as m<DCE, which is 38°.
The 142° angle is an exterior angle to triangle, DCE, an exterior angles are the sum of the remote interior angles, which are <CDE and <DEC. Therefore, we can write:
142° = m<CDE + m<DEC
And we can substitute the values we have:
142° = 38° + x
x = 104°
