Answers

1. 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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2. 9514 1404 393

   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°

   Reply