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.

   Zee sees a ladder's parallel rails crossed by a strap. Angle 4 is (2x + 25)° and angle 5 is (3x − 15)°. How many degrees is angle 4?

   105
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.

   Milo draws two parallel lines and a crossing line on paper. Angle 2 is (5x − 30)° and angle 8 is (3x + 10)°. How many degrees is angle 2?

   95
4. 4.

   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
5. 5.

   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
6. 6.

   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
7. 7.

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

   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
9. 9.

   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 the same size as angle 4, and angle 4 is next to angle 6, so they match
   • Because angle 3 is equal to its corresponding angle 7, and angle 7 is vertical to angle 6
10. 10.

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

    • Because sliding the top track down the road puts it on the bottom track, and angle 2 lands on angle 6
    • 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