Question

If anyone can help me to solve this.​

Answer 1

`\boxed {1) 90^(o)}\\\boxed {2) 80^(o)}`

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°

Answer 2

1) x + 96 = 90°

2) x + 89 = 80°

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 circled on the diagram, 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 circled on the diagram:

⇒ x + 96 = -6 + 96 = 90°

⇒ x + 96 = 90°

Question 2

To find the measure of the angle circled on the diagram, 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 circled on the diagram:

⇒ x + 89 = -9 + 89

⇒ x + 89 = 80°