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Alexxx [7]
2 years ago
15

Find the value of x, if C is on line AE

Mathematics
2 answers:
murzikaleks [220]2 years ago
3 0

Answer:

x = 11°

Step-by-step explanation:

<u>Linear Pair</u>

Two angles adjacent to each other that form a straight line.

The sum of angles of a linear pair is always equal to 180°.

⇒ m∠C = 180° - 33° = 147°

<u>Alternate Interior Angle Theorem</u>

When two parallel lines are cut by a transversal, the alternate interior angles are congruent.

From inspection of the diagram, we can see that AB ║ DC.

Therefore, AE is the transversal.

So m∠A = 33°

<u>Sum of interior angles of a triangle is 180°</u>

Therefore, the top angle of the triangle = 180° - m∠A - 2x

                                                                  = 180° - 33° - 2x              

                                                                   = 147° - 2x

<u>Angles around a point add up to 360°</u>

⇒ 33° + m∠C + 5x + (147° - 2x) = 360°

⇒ 33° + 147° + 5x + 147° - 2x = 360°

⇒ 327° + 3x = 360°

⇒ 3x = 33°

⇒ x = 11°

guapka [62]2 years ago
3 0

Answer:

x = 11°

Explanation:

  • m∠C = m∠A = 33°
  • m∠B = 2(x)
  • m∠I = 180° - 5(x)

============                       [ total interior angle in a triangle is 180° ]

<u>solve for x</u>

  • 33° + 2(x) + 180° - 5(x) = 180°
  • -3(x) = 180° - 213°
  • -3(x) = -33°
  • x = 11°
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