Angles made by a transversal: solve for x

Answer Key - Grade 10 Math Worksheet - Building Confidence

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

2. 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
3. 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
4. 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
5. 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
6. 5.

   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.

   85
7. 6.

   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.

   58
8. 7.

   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.

   137
9. 8.

   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.

   141
10. 9.

    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.

    79
11. 10.

    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.

    93