Which angle pairs prove that two lines are parallel?

Answer Key - Grade 10 Math Worksheet - Building Confidence

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

2. 1.

   Milo checks the two rails of a ladder. ∠DGH and ∠GHQ are same-side interior angles, m∠DGH = 68° and m∠GHQ = 112°. Is line DF parallel to line QS?

   • No: same-side interior angles must be equal.
   • Yes: the angles add to 180°.
   • No: 112° is an obtuse angle.
3. 2.

   Noah checks two window bars. ∠FGH and ∠GHQ are alternate interior angles, m∠FGH = 64° and m∠GHQ = 66°. Is line DF parallel to line QS?

   Use the picture in question 1.

   • No: alternate interior angles must add to 180°.
   • No: 64° and 66° are not equal.
   • Yes: the lines look parallel in the sketch.
4. 3.

   Ren draws two lines on paper. Which fact proves that line DF ∥ line QS?

   Use the picture in question 1.

   • m∠UGD = m∠FGH
   • m∠DGH = m∠GHQ
   • m∠UGF = m∠GHS
   • m∠UGF + m∠FGH = 180°
5. 4.

   Tala checks two bike lanes. Which fact proves that line DF ∥ line QS?

   Use the picture in question 1.

   • m∠FGH = m∠GHS
   • m∠DGH = m∠GHS
   • m∠GHQ + m∠QHV = 180°
   • m∠QHV = m∠GHS
6. 5.

   Zee checks two stripes on a rug. Which fact proves that line DF ∥ line QS?

   Use the picture in question 1.

   • m∠FGH + m∠UGF = 180°
   • m∠UGD = m∠UGF
   • m∠FGH + m∠GHS = 180°
   • m∠FGH + m∠GHQ = 180°
7. 6.

   Ari draws two lines in crayon. Which fact proves that line DF ∥ line QS?

   Use the picture in question 1.

   • m∠UGD = m∠SHV
   • m∠UGD = m∠FGH
   • m∠SHV = m∠QHV
   • m∠UGD + m∠SHV = 180°
8. 7.

   Bo checks two guitar strings. ∠DGH and ∠GHQ are same-side interior angles, and m∠DGH = 81°. What must m∠GHQ be for DF ∥ QS, in degrees?

   Use the picture in question 1.

   99
9. 8.

   Esme draws two lines on paper. ∠FGH and ∠GHS are same-side interior angles, and m∠FGH = 116°. What must m∠GHS be for DF ∥ QS, in degrees?

   Use the picture in question 1.

   64
10. 9.

    Jun checks two bike lanes. ∠UGD and ∠QHV are same-side exterior angles, and m∠UGD = 72°. What must m∠QHV be for DF ∥ QS, in degrees?

    Use the picture in question 1.

    108
11. 10.

    Kira checks two window bars. ∠UGF and ∠SHV are same-side exterior angles, and m∠UGF = 127°. What must m∠SHV be for DF ∥ QS, in degrees?

    Use the picture in question 1.

    53