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