Angles made by a line crossing parallel lines

Answer Key - Grade 8 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Ari draws two parallel lines and a crossing line on paper. Angle 2 is (2x + 10)° and angle 6 is (4x − 40)°. How many degrees is angle 2?

   60
2. 2.

   Noah draws triangle CDF and a line through the top corner F parallel to the base. The base angles are 47° and 66°. How many degrees is the angle at F?

   67
3. 3.

   Pia draws triangle GHQ and a line through the top corner Q parallel to the base. The base angles are 38° and 77°. How many degrees is the angle at Q?

   65
4. 4.

   Ren draws triangle SUV and a line through the top corner V parallel to the base. The base angles are 55° and 52°. How many degrees is the angle at V?

   73
5. 5.

   Zee draws two parallel lines and a crossing line with a crayon. Angle 4 is (3x + 20)° and angle 5 is (5x − 40)°. Which equation finds x?

   • 3x + 20 = 5x − 40
   • 3x + 20 + 5x − 40 = 180
   • 3x + 20 = 5x + 40
6. 6.

   Ari sees a ladder's parallel rails crossed by a strap. Angle 3 is (2x + 15)° and angle 5 is (4x − 9)°. Which equation finds x?

   • 2x + 15 − 4x − 9 = 180
   • 2x + 15 + 4x − 9 = 180
   • 2x + 15 = 4x − 9
7. 7.

   Jun draws two parallel lines and a crossing line. Why are alternate interior angles 3 and 6 equal?

   • Because angle 3 and angle 6 are on a straight line, and a straight line is 180°
   • Because angle 3 is equal to its corresponding angle 7, and angle 7 is vertical to angle 6
   • Because angle 3 is the same size as angle 4, and angle 4 is next to angle 6, so they match
8. 8.

   Kira draws two parallel lines and a crossing line. Why do same-side interior angles 3 and 5 add to 180°?

   • Because the lines are parallel, and parallel lines make angle pairs add to 180°, so these do too
   • Because angle 3 is equal to its corresponding angle 7, and angles 7 and 5 make a straight line
   • Because angle 3 is on the same side as angle 5, and angles on one side are equal
9. 9.

   Milo draws two parallel lines and a crossing line. Why are alternate exterior angles 1 and 8 equal?

   • Because angle 1 is equal to its corresponding angle 5, and angle 5 is vertical to angle 8
   • Because angle 1 and angle 8 are both outside the lines, and outside angles are equal, so they match
   • Because angle 1 and angle 8 are on the same side, and angles on one side add to 180°
10. 10.

    Noah rides a bike past two parallel paths crossed by a trail. Why do same-side exterior angles 2 and 8 add to 180°?

    • Because angle 2 is on the same side as angle 8, and angles on one side are equal
    • Because the paths are parallel, and parallel paths make angle pairs add to 180°, so these do too
    • Because angle 2 is equal to its corresponding angle 6, and angles 6 and 8 make a straight line