Grade 10 · Math · Geometry

10th grade Angles made by a transversal: solve for x worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Angles made by a transversal: solve for x

Grade 10 Math Worksheet - Building Confidence

NameDate

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

1.
Ari draws two parallel rails DF and QS crossed by a road UV. Why is m∠FGH = m∠GHQ?
- Alternate interior angles are equal
- Same-side interior angles add to 180°
- Vertical angles are equal
- Corresponding angles are equal
2.
Bo draws two parallel rails DF and QS crossed by a road UV. Why do m∠DGH and m∠GHQ add to 180°?
Use the picture in question 1.
- Corresponding angles are equal
- Same-side interior angles add to 180°
- Angles in a linear pair add to 180°
- Alternate interior angles are equal
3.
Esme draws two parallel rails DF and QS crossed by a road UV. Why is m∠UGF = m∠QHV?
Use the picture in question 1.
- Vertical angles are equal
- Corresponding angles are equal
- Alternate exterior angles are equal
- Alternate interior angles are equal
4.
Jun draws two parallel rails DF and QS crossed by a road UV. Why is m∠DGH = m∠QHV?
Use the picture in question 1.
- Alternate interior angles are equal
- Alternate exterior angles are equal
- Same-side interior angles add to 180°
- Corresponding angles are equal
Luz draws two parallel road lines DF and QS crossed by a line UV. m∠FGH = (4x + 7)° and m∠GHS = (3x + 19)°. What is m∠GHS, in degrees?
Use the picture in question 1.
Milo draws two parallel tracks DF and QS crossed by a line UV. m∠UGF = (5x − 12)° and m∠GHS = (3x + 16)°. What is m∠GHS, in degrees?
Use the picture in question 1.
Pia draws parallel rails DF and QS crossed by a road UV. m∠UGF = (3x + 4)° and m∠QHV = (5x − 22)°. What is m∠FGH, in degrees?
Use the picture in question 1.
Ren draws parallel rails DF and QS crossed by a road UV. m∠DGH = (2x + 15)° and m∠GHS = (4x − 9)°. What is m∠FGH, in degrees?
Use the picture in question 1.
Tala draws parallel rails DF and QS crossed by a road UV. m∠FGH = (6x + 5)° and m∠GHS = (4x + 15)°. What is m∠UGF, in degrees?
Use the picture in question 1.
Zee draws parallel rails DF and QS crossed by a road UV. m∠UGD = (7x − 11)° and m∠GHQ = (4x + 31)°. What is m∠DGH, in degrees?
Use the picture in question 1.

10th grade Angles made by a transversal: solve for x worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Angles made by a transversal: solve for x. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can decide which lines are parallel from measured angles, name the pair and say which converse applies.
I can fill the missing reason or statement in a short proof, and tell a theorem from its converse.
I can find a counterexample, or one measurement, that shows lines are not parallel.

Standard: G-CO.C.9

Words to know

transversal: A line that crosses two other lines (here line UV).

interior / exterior: Between the two parallel lines / outside them.

corresponding angles: Same place at each crossing (both upper right). Equal when lines are parallel.

alternate angles: Opposite sides of the transversal, one at each crossing. Equal.

same-side angles: Same side of the transversal, one at each crossing. Add to 180°.

∠DGH: The angle with its corner at G, between rays GD and GH.

DF ∥ QS: Line DF is parallel to line QS (arrows on the sketch).

Common mistakes

Your child mixed up alternate angles (opposite sides of the road) with corresponding angles (same place at each crossing). Name the two sides first.

Your child mixed up alternate angles (equal) with same-side angles (add to 180°).

Your child mixed up angles between the rails (interior) with angles outside them (exterior). Trace the rails with a finger.

What to say

Ask: are the two angles on the same side of the road?

Questions parents ask

What is the most common mistake with angles made by a transversal: solve for x?

Your child mixed up alternate angles (opposite sides of the road) with corresponding angles (same place at each crossing). Name the two sides first.

Are these 10th 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 geometry

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