If m angle cdf equals (3x +14), m angle fde(5x-2), and m angle cde= (10x- 18)

x = 15 , m∠ CDF = 59° , m∠FDE = 73° , m∠CDE = 132°

Step-by-step explanation:

* Lets explain how to solve the problem

- The m∠ CDF = (3x + 14)°

- The m∠ FDE = (5x - 2)°

- The m∠ CDE = (10x - 18)°

- We need to find the value of x and the measure of each angle

∵ Point D is the vertex of the three angles

∵ The ray DF is between the rays DC and DE

∴ m∠ CDE = m∠ CDF + m∠ FDE

∵ m∠ CDE = (10x - 18)°

∵ m∠ CDF = (3x + 14)°

∵ m∠ FDE = (5x - 2)°

- Substitute the measures of these angles in the equation above

∴ 10x - 18 = (3x + 14) + (5x - 2)

- Add the like terms in the right hand side

∴ 10x - 18 = (3x + 5x) + (14 - 2)

∴ 10x - 18 = 8x + 12

- Subtract 8x from both sides and add 18 to both sides

∴ 10x - 8x = 12 + 18

∴ 2x = 30

- Divide both sides by 2

∴ x = 15

- Substitute the value of x in the measure of each angle to find it

∴ m∠ CDF = 3(15) + 14 = 59°

∴ m∠ FDE = 5(15) - 2 = 73°

∴ m∠ CDE = 10(15) -18 = 132°

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!