Before attempting to solve this question, we must first know three things.
1. A straight line has a measure of 180 degrees.
2. When two angles add up to 180 degrees, those angles are called supplementary.
3. The interior angles of a triangle add up to 180 degrees.
We can see ∠ECT = 180 degrees.
∠DCT is supplementary to ∠DCE.
∠DCT = 140 degreees
∠DCE = x degrees
x + 140 = 180
Solve for x.
x + 140 = 180
x = 40 <-- Subtract 140 from each side
∠DCE = 40 degrees
We know the two interior angles of ΔDEC.
45 + 40 + x = 180
Solve for x.
45 + 40 + x = 180
85 + x = 180 <-- Combine like terms
x = 95
So, the missing angle is equal to 95 degrees.
