Angles made by a line crossing parallel lines
Grade 8 Math Worksheet

Circle the best answer, or write your answer on the line.
Milo draws two parallel lines and a crossing line on paper. Angle 6 is 127°. How many degrees is angle 4?
Ren draws two parallel lines and a crossing line with a pencil. Angle 1 is 109°. How many degrees is angle 6?
Two parallel lines (marked with arrows) are cut by a crossing line. At the top crossing the angles are 1 (upper-left), 2 (upper-right), 3 (lower-left) and 4 (lower-right); the bottom crossing is numbered 5 to 8 the same way (sketch, not to scale). Angle 1 is upper-left at the top crossing, and angle 6 is upper-right at the bottom crossing. Angle 1 and angle 6 are not a named pair: one more angle links them. Two parallel lines (marked with arrows) are cut by a crossing line. At the top crossing the angles are 1 (upper-left), 2 (upper-right), 3 (lower-left) and 4 (lower-right); the bottom crossing is numbered 5 to 8 the same way (sketch, not to scale). Angle 1 is upper-left at the top crossing, and angle 6 is upper-right at the bottom crossing. Angle 1 and angle 6 are not a named pair: one more angle links them. 1 2 3 4 5 6 7 8 Angle 1 and angle 6 are not a named pair: one more angle links them. Not to scale. Tala rides a bike past two parallel paths crossed by a trail. Angle 2 is 76°. How many degrees is angle 5?
Two parallel lines (marked with arrows) are cut by a crossing line. At the top crossing the angles are 1 (upper-left), 2 (upper-right), 3 (lower-left) and 4 (lower-right); the bottom crossing is numbered 5 to 8 the same way (sketch, not to scale). Angle 2 is upper-right at the top crossing, and angle 5 is upper-left at the bottom crossing. Angle 2 and angle 5 are not a named pair: one more angle links them. Two parallel lines (marked with arrows) are cut by a crossing line. At the top crossing the angles are 1 (upper-left), 2 (upper-right), 3 (lower-left) and 4 (lower-right); the bottom crossing is numbered 5 to 8 the same way (sketch, not to scale). Angle 2 is upper-right at the top crossing, and angle 5 is upper-left at the bottom crossing. Angle 2 and angle 5 are not a named pair: one more angle links them. 1 2 3 4 5 6 7 8 Angle 2 and angle 5 are not a named pair: one more angle links them. Not to scale. Zee draws two parallel lines and a crossing line with a crayon. Angle 3 is 67°. How many degrees is angle 8?
Two parallel lines (marked with arrows) are cut by a crossing line. At the top crossing the angles are 1 (upper-left), 2 (upper-right), 3 (lower-left) and 4 (lower-right); the bottom crossing is numbered 5 to 8 the same way (sketch, not to scale). Angle 3 is lower-left at the top crossing, and angle 8 is lower-right at the bottom crossing. Angle 3 and angle 8 are not a named pair: one more angle links them. Two parallel lines (marked with arrows) are cut by a crossing line. At the top crossing the angles are 1 (upper-left), 2 (upper-right), 3 (lower-left) and 4 (lower-right); the bottom crossing is numbered 5 to 8 the same way (sketch, not to scale). Angle 3 is lower-left at the top crossing, and angle 8 is lower-right at the bottom crossing. Angle 3 and angle 8 are not a named pair: one more angle links them. Two parallel lines (marked with arrows) are cut by a crossing line. 1 2 3 4 5 6 7 8 Angle 3 and angle 8 are not a named pair: one more angle links them. Not to scale. Jun draws two parallel lines and a crossing line on paper. Which statement is true about angle 2 and angle 7?
Two parallel lines (marked with arrows) are cut by a crossing line. At the top crossing the angles are 1 (upper-left), 2 (upper-right), 3 (lower-left) and 4 (lower-right); the bottom crossing is numbered 5 to 8 the same way (sketch, not to scale). Angle 2 is upper-right at the top crossing, and angle 7 is lower-left at the bottom crossing. Two parallel lines (marked with arrows) are cut by a crossing line. At the top crossing the angles are 1 (upper-left), 2 (upper-right), 3 (lower-left) and 4 (lower-right); the bottom crossing is numbered 5 to 8 the same way (sketch, not to scale). Angle 2 is upper-right at the top crossing, and angle 7 is lower-left at the bottom crossing. 1 2 3 4 5 6 7 8 Not to scale. - Equal: they are corresponding angles
- They add to 180°: they are same-side exterior angles
- Equal: they are alternate exterior angles
Milo draws two parallel lines and a crossing line with a pencil. Angle 1 is (3x − 6)° and angle 5 is 66°. What is x?
Two parallel lines (marked with arrows) are cut by a crossing line. At the top crossing the angles are 1 (upper-left), 2 (upper-right), 3 (lower-left) and 4 (lower-right); the bottom crossing is numbered 5 to 8 the same way (sketch, not to scale). Angle 1 is upper-left at the top crossing, and angle 5 is upper-left at the bottom crossing. Two parallel lines (marked with arrows) are cut by a crossing line. At the top crossing the angles are 1 (upper-left), 2 (upper-right), 3 (lower-left) and 4 (lower-right); the bottom crossing is numbered 5 to 8 the same way (sketch, not to scale). Angle 1 is upper-left at the top crossing, and angle 5 is upper-left at the bottom crossing. 1 2 3 4 5 6 7 8 Not to scale. Noah rides a bike past two parallel paths crossed by a trail. Angle 4 is (4x + 8)° and angle 8 is 108°. What is x?
Two parallel lines (marked with arrows) are cut by a crossing line. At the top crossing the angles are 1 (upper-left), 2 (upper-right), 3 (lower-left) and 4 (lower-right); the bottom crossing is numbered 5 to 8 the same way (sketch, not to scale). Angle 4 is lower-right at the top crossing, and angle 8 is lower-right at the bottom crossing. Two parallel lines (marked with arrows) are cut by a crossing line. At the top crossing the angles are 1 (upper-left), 2 (upper-right), 3 (lower-left) and 4 (lower-right); the bottom crossing is numbered 5 to 8 the same way (sketch, not to scale). Angle 4 is lower-right at the top crossing, and angle 8 is lower-right at the bottom crossing. 1 2 3 4 5 6 7 8 Not to scale. Pia rides a bike past two parallel paths crossed by a trail. Angle 6 is (3x + 18)° and angle 4 is 114°. What is x?
Two parallel lines (marked with arrows) are cut by a crossing line. At the top crossing the angles are 1 (upper-left), 2 (upper-right), 3 (lower-left) and 4 (lower-right); the bottom crossing is numbered 5 to 8 the same way (sketch, not to scale). Angle 6 is upper-right at the bottom crossing, and angle 4 is lower-right at the top crossing. Two parallel lines (marked with arrows) are cut by a crossing line. At the top crossing the angles are 1 (upper-left), 2 (upper-right), 3 (lower-left) and 4 (lower-right); the bottom crossing is numbered 5 to 8 the same way (sketch, not to scale). Angle 6 is upper-right at the bottom crossing, and angle 4 is lower-right at the top crossing. Two parallel lines (marked with arrows) are cut by a crossing line. 1 2 3 4 5 6 7 8 Not to scale. Tala sees a ladder's parallel rails crossed by a strap. Angle 2 is (4x − 12)° and angle 8 is 100°. What is x?
Two parallel lines (marked with arrows) are cut by a crossing line. At the top crossing the angles are 1 (upper-left), 2 (upper-right), 3 (lower-left) and 4 (lower-right); the bottom crossing is numbered 5 to 8 the same way (sketch, not to scale). Angle 2 is upper-right at the top crossing, and angle 8 is lower-right at the bottom crossing. Two parallel lines (marked with arrows) are cut by a crossing line. At the top crossing the angles are 1 (upper-left), 2 (upper-right), 3 (lower-left) and 4 (lower-right); the bottom crossing is numbered 5 to 8 the same way (sketch, not to scale). Angle 2 is upper-right at the top crossing, and angle 8 is lower-right at the bottom crossing. 1 2 3 4 5 6 7 8 Not to scale. Zee draws two parallel lines and a crossing line with a crayon. The crossing line is square to the parallel lines, so angle 2 is 90°. How many degrees is angle 7?
Two parallel lines (marked with arrows) are cut by a crossing line. At the top crossing the angles are 1 (upper-left), 2 (upper-right), 3 (lower-left) and 4 (lower-right); the bottom crossing is numbered 5 to 8 the same way (sketch, not to scale). Angle 2 is upper-right at the top crossing, and angle 7 is lower-left at the bottom crossing. Two parallel lines (marked with arrows) are cut by a crossing line. At the top crossing the angles are 1 (upper-left), 2 (upper-right), 3 (lower-left) and 4 (lower-right); the bottom crossing is numbered 5 to 8 the same way (sketch, not to scale). Angle 2 is upper-right at the top crossing, and angle 7 is lower-left at the bottom crossing. 1 2 3 4 5 6 7 8 Not to scale. - 45°: half of a square corner
- 180°: angles 2 and 7 lie along one line
- 90°: it matches angle 2, a square corner