Question

Apply. Streets A and L run parallel to each other. Boulevard N forms a 75 degree angle with Street L south of (below) their intersection. What angle does Boulevard N make with Street L north of (above) their intersection. Justify your answer

Answer 1

There are two street A and L which run parallel to each other.

Suppose the point of intersection of Boulevard N and Street L is 75°south of below their intersection.

Let their point of intersection is S.

Taking a point P and Q on opposite side of L and R and T on opposite side of Line N,

then either ∠PSR=75° or ∠ QSR=75°

Case 1. If ∠PSR=75°,

then ∠PSR + ∠PST=180°[ linear pair]

75°+ ∠PST=180°

∠PST=180°- 75°

∠PST=105°

∠QST = ∠PSR=75° [ Vertically opposite angles]

2. If ∠ Q S R =75°

∠ Q S R + ∠ Q S T=180°[linear pair]

75° +∠ Q S T=180°

∠ Q S T=180°-75°

∠ Q S T= 105°

∠Q SR = ∠P ST = 75° [ Vertically opposite angles]