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°

for finding the midpoint of any given 2 pair of points simply add the respective x coordinates with other x coordinate and the y coordinate with other y coordinate and divide them by 2

in your question it will be :

(3+1)/2 for the x coordinate of mid point i.e 2

[8+(-4)]/2 for the y coordinate of midpoint i.e 2

so coordinates of mid point of points (3,8) and (1,-4) will be (2,2)

the answer is 844

step-by-step explanation:

it is 844 because if you add 836.50 + 7.5 you will get 844