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.

   Esme draws two parallel lines and a crossing line with a pencil. Angle 3 is (2x + 30)° and angle 7 is (3x + 10)°. How many degrees is angle 3?

   70
2. 2.

   Jun rides a bike past two parallel paths crossed by a trail. Angle 3 is (3x − 25)° and angle 5 is (4x − 40)°. How many degrees is angle 3?

   80
3. 3.

   Kira draws two parallel lines and a crossing line with a crayon. Angle 4 is (4x − 15)° and angle 6 is (5x − 30)°. How many degrees is angle 4?

   85
4. 4.

   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
5. 5.

   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
6. 6.

   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
7. 7.

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

   • 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
   • Because angle 3 and angle 6 are on a straight line, and a straight line is 180°
8. 8.

   Luz watches a toy train on two parallel rails crossed by a road. Why are corresponding angles 2 and 6 equal?

   • Because angle 2 and angle 6 are on a straight line, and a straight line is 180°
   • Because angle 2 and angle 6 are across from each other, and across angles are vertical
   • Because sliding the top track down the road puts it on the bottom track, and angle 2 lands on angle 6
9. 9.

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

   • Because angle 1 and angle 8 are on the same side, and angles on one side add to 180°
   • 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
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 the paths are parallel, and parallel paths make angle pairs add to 180°, so these do too
    • Because angle 2 is on the same side as angle 8, and angles on one side are equal
    • Because angle 2 is equal to its corresponding angle 6, and angles 6 and 8 make a straight line