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Answer:

x + 96 = 90°

x + 89 = 80°

Step-by-step explanation:

Consecutive Interior Angles Theorem

When a transversal line intersects two parallel lines, it forms two pairs of consecutive angles on either side of the transversal line.  Each pair of consecutive interior angles are supplementary (sum to 180°).

Question 1

To find the measure of the angle, find the value of x by using the Consecutive Interior Angle Theorem:

⇒ (x + 96)° + (x + 96)° = 180°

⇒ x + 96 + x + 96 = 180

⇒ 2x + 192 = 180

⇒ 2x + 192 - 192 = 180 - 192

⇒ 2x = -12

⇒ 2x ÷ 2 = -12 ÷ 2

⇒ x = -6

Substitute the found value of x into the expression to find the measure of the angle indicated in bold:

⇒ x + 96 = -6 + 96 = 90°

Question 2

To find the measure of the angle, find the value of x by using the Consecutive Interior Angle Theorem:

⇒ (x + 109)° + (x + 89)° = 180°

⇒ x + 109 + x + 89 = 180

⇒ 2x + 198 = 180

⇒ 2x + 198 - 198 = 180 - 198

⇒ 2x = -18

⇒ 2x ÷ 2 = -18 ÷ 2

⇒ x = -9

Substitute the found value of x into the expression to find the measure of the angle indicated in bold:

⇒ x + 89 = -9 + 89 = 80°

Answer:

[tex]\boxed {1) 90^{o}}\\\boxed {2) 80^{o}}[/tex]

Step-by-step explanation:

Part 1 :

  • x + 96 + x + 96 = 180 (angle pairs of a line)
  • 2x + 192 = 180
  • 2x = -12
  • x = -6

  • ∠ = -6 + 96
  • ∠ = 90°

Part 2 :

  • x + 109 + x + 89 = 180 (same reason)
  • 2x + 198 = 180
  • 2x = -18
  • x = -9

  • ∠ = -9 + 89
  • ∠ = 80°
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