Answer:
α + β + Φ = 360°
Explanation:
If we draw a horizontal line that is parallel to L₁ and L₂ and that passes through the vertex of angle β, we create two sets of consecutive interior angles (see attachment).
Since consecutive angles are supplementary (sum to 180°) then:
- Φ + β₁ = 180°
- β₂ + α = 180°
Therefore, the sum of these angles is 360°:
α + β + Φ
= Φ + β + α
= Φ + β₁ + β₂ + α
= 180° + 180°
= 360°
Hence proving that α + β + Φ = 360°.