Question

How do I solve this question?

Answer 1

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.