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.

   Bo watches a toy train on two parallel rails crossed by a road. Angle 1 is (2x + 25)° and angle 8 is (5x − 20)°. How many degrees is angle 1?

   55
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.

   Tala draws triangle WYC and a line through the top corner C parallel to the base. The base angles are 29° and 85°. How many degrees is the angle at C?

   66
6. 6.

   Bo draws two parallel lines and a crossing line on paper. Angle 2 is (6x − 8)° and angle 6 is (4x + 20)°. Which equation finds x?

   • 6x − 8 + 4x + 20 = 180
   • 6x − 8 = 4x − 20
   • 6x − 8 = 4x + 20
7. 7.

   Esme watches a toy train on two parallel rails crossed by a road. Angle 1 is (5x − 5)° and angle 7 is (3x + 25)°. Which equation finds x?

   • 5x − 5 + 3x + 25 = 180
   • 5x − 5 = 3x + 25
   • 5x − 5 − 3x + 25 = 180
8. 8.

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

   • 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
   • Because the lines are parallel, and parallel lines make angle pairs add to 180°, so these do too
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 on the same side, and angles on one side add to 180°
   • Because angle 1 and angle 8 are both outside the lines, and outside angles are equal, so they match
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