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Answer:

x = 18°, ∠A = 110°

Explanation:

As the lines are parallel, their sums of total interior angle is 180°

∠A + ∠B = 180°

5x +20° +9x-92° = 180°

14x -72° = 180°

14x = 180° + 72°

14x = 252°

x = 18°

Solve for angle A:

∠A = 5x +20°

∠A = 5(18) +20

∠A = 110°

Solution:

Note that:

  • ∠A = 5x + 20
  • ∠B = 9x - 92
  • ∠A + ∠B = 180°

Use the equation "∠A + ∠B = 180°" to solve for x and ∠A.

  • ∠A + ∠B = 180°
  • => 5x + 20 + 9x - 92 = 180
  • => 14x - 72 = 180
  • => 14x = 252
  • => x = 252/14
  • => x = 18

Now, find ∠A.

  • ∠A = 5x + 20
  • => ∠A = 5(18) + 20
  • => ∠A = 90 + 20
  • => ∠A = 110°

Hoped this helped!

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