Answer:
∠1 = 135°
∠2 = 45°
∠3 = 45°
∠4 = 135°
∠5 = 135°
∠6 = 45°
∠7 = 45°
∠8 = 135°
Step-by-step explanation:
- The diagram shows two lines that are intersected by a transversal. (A transversal is a line that passes through two lines in the same plane at two distinct points).
- When two lines are intersected by a transversal, the angles in matching corners are called Corresponding Angles
So ∠1 = ∠5 , ∠2 = ∠6 , ∠3 = ∠7 , ∠4 = ∠8
- Angles on one side of a straight line always add to 180°
Using the Angles on a Straight Line theorem
Angle 1 and 2 are on a straight line, so
∠2 = 180 - ∠1 = 180 - 135 = 45°
Similarly,
∠3 = 180 - ∠1 = 180 - 135 = 45°
∠4 = 180 - ∠3 = 180 - 45 = 135°
Using the Corresponding Angles theorem
As ∠1 = ∠5, then ∠5 = 135°
As ∠2 = ∠6, then ∠6 = 45°
As ∠3 = ∠7, then ∠7 = 45°
As ∠4 = ∠8, then ∠8 = 135°
