Question

Find the value of x. Give reasons to justify your solution. C ∈ AE

Answer 1

Answer:

x = 11º

Step-by-step explanation:

1. Notice Parallel Lines

2. Understand Angle Relationships When Parallel Lines Are Present (e.g., alternate interior/exterior)

3. ∠CAB ≅ ∠DCA ∴ m∠CAB = 33º

4. Use exterior angle theorem: the sum of non-adjacent angles of the same triangle which the exterior angle is drawn is equal to the measure of that angle.

5. Therefore write and solve the equation 2x + 33º (sum of non-adjacent interior angles) = 5x (exterior angle).

• 2x + 33 = 5x (C.L.T or Combine Like Terms)
• 3x = 33 (inverse operations; divide by 3)
• x = 11º (remember to apply units)