Question

D

(13y + 3)º
(5y + 5)
116°F
E
Use the Exterior Angle Theorem to find the measure of each angle.
mic
m_D =
m_DEC =

Answer 1

The answer to this question is

Angle at C is 35

Angle at D is 81

Angle at E is 64

because y=6

Answer 2

∠C = 35

∠D = 81

∠DEC = 64

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