Answer:
Answer:
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°
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Answer:
∠CDF = 59°
∠FDE = 73°
∠CDE = 132°
Step-by-step explanation:
We can use the angle sum theorem to relate the angles:
∠CDF + ∠FDE = ∠CDE
(3x +14) +(5x -2) = (10x -18) . . . . . divide by " (presumably, degrees (°))
8x +12 = 10x -18 . . . . . collect terms
30 = 2x . . . . . . . . . . . . add 18-8x
15 = x . . . . . . . . . . . . . . divide by 2
Then the angle measures are ...
∠CDF = (3x +14)° = (3(15) +14)° = 59°
∠FDE = (5x -2)° = (5(15) - 2)° = 73°
∠CDE = (10x -18)° = (10(15) -18)° = 132°
