In the parking lot shown, the lines that mark the width of each space

1.	In the parking lot shown, the lines that mark the width of each space are parallel. If ∠1 = (2x – 3y)°; ∠2 = (x + 39)° find x° and y°.
Answer» From the picture ∠2 + 65° = 180° [Sum of interior angles on the same side of a transversal] x + 39° + 65° = 180° x + 104° = 180° x + 104° – 104° = 180° – 104° x = 76° Also from the picture ∠1 = 65° [alternate exterior angles] 2x – 3y = 65° 2 (76) – 3y = 65° 152° – 3y = 65° 152° – 3y – 152° = 65 – 152° -3y = -87 y = \(\frac{-87}{-3}\) y = 29° x = 76°; y = 29°

In the parking lot shown, the lines that mark the width of each space are parallel. If ∠1 = (2x – 3y)°; ∠2 = (x + 39)° find x° and y°.

Answer»

From the picture

∠2 + 65° = 180° [Sum of interior angles on the same side of a transversal]

x + 39° + 65° = 180°

x + 104° = 180°

x + 104° – 104° = 180° – 104°

x = 76°

Also from the picture

∠1 = 65° [alternate exterior angles]

2x – 3y = 65°

2 (76) – 3y = 65°

152° – 3y = 65°

152° – 3y – 152° = 65 – 152°

-3y = -87

y = \(\frac{-87}{-3}\)

y = 29°

x = 76°; y = 29°