Answer:
∠C = 35
∠D = 81
∠DEC = 64
Step-by-step explanation:
Exterior angle theorem - An exterior angle of a triangle is equal to the opposite interior angles of a triangle.
∠DEF is an exterior angle of ΔCED
∠DCE and ∠ CDE are opposite interior angles of ∠DEF
That being said we know that ∠C + ∠D = ∠DEF
We will use this as our equation
* plug in the information we are given about each angle into the equation *
5y + 5 + 13y + 3 = 116
Now we solve for y using basic algebra
step 1 combine like terms
5y + 13y = 18y
5 + 3 = 8
now we have 18y + 8 = 116
step 2 subtract 8 from each side
8 - 8 cancels out
116 - 8 = 108
now we have 18y = 108
step 3 divide each side by 18
18y / 18 cancels out
108 / 18 = 6
we're left with y = 6
Now to find the measures of ∠C and ∠ D
To find the measure of each we replace " y " in the given expression with 6
For ∠C
5y + 5
* replace y with 6 *
5(6) + 5
5(6) = 30
30 + 5 = 35
Hence ∠C = 35
For ∠D
13y + 3
* replace y with 6 *
13(6) + 3
13(6) = 78
78 + 3 = 81
Hence ∠D = 81
Finally we want to find ∠DEC
We can do this by using the triangle angle rule which states that the angles of a triangle should add up to equal 180
so to find the missing angle we subtract the given angles ( 81 and 35 ) from 180
so ∠DEC = 180 - 81 - 35
180 - 81 - 35 = 64
Hence ∠DEC = 64
