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8th grade Angles made by a line crossing parallel lines worksheet

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Angles made by a line crossing parallel lines

Grade 8 Math Worksheet - Challenge Me

NameDate

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

  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?

  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?

  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?

  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?

  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?

  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?

  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. 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. 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. 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
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8th grade Angles made by a line crossing parallel lines worksheet – printable
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About this worksheet

Angles made by a line crossing parallel lines. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can name the pairs of angles made when a line crosses two parallel lines, and say which are equal and which add to 180°.
  • I can find any of the eight angles from one of them, and write and solve an equation for x when the angles are written with x.
  • I can explain why alternate interior angles are equal and why same-side interior angles add to 180°.

Standard: 8.G.A.5 (parallel lines cut by a transversal)

Words to know

parallel lines: Two lines that never meet and stay the same distance apart. Arrows mark them.

crossing line (transversal): A line that crosses two or more other lines.

interior angles: The four angles between the two parallel lines.

exterior angles: The four angles outside the two parallel lines.

corresponding angles: In the same place at each crossing, like both upper-right. They are equal.

alternate angles: On opposite sides of the crossing line, one at each line. They are equal.

same-side angles: On the same side of the crossing line, one at each line. They add to 180°.

straight line: A line with no bend. Angles side by side along it add to 180°.

Common mistakes

Thought angles that are equal add to 180°. Between parallel lines, corresponding, alternate interior and alternate exterior angles are equal.

Thought angles that add to 180° are equal. Between parallel lines, same-side angles add to 180°.

Used 90° (a square corner) where same-side angles between parallel lines add to 180°.

What to say

Ask: are these two angles in the same place at the two crossings, or on a straight line together?

Ask: is one of the angles big (wide) and the other small (narrow)? Can two equal angles look like that?

Ask: do these two angles together make a square corner or a straight line?

Questions parents ask

What is the most common mistake with angles made by a line crossing parallel lines?

Thought angles that are equal add to 180°. Between parallel lines, corresponding, alternate interior and alternate exterior angles are equal.

How can I help my child with angles made by a line crossing parallel lines?

Ask: are these two angles in the same place at the two crossings, or on a straight line together?

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 8 math

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