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Geometry

Parallel Lines and Transversals

Lesson

When a transversal crosses two parallel lines, it creates 8 angles — and only two distinct measures. Memorize which pairs are equal and which are supplementary.

Equal pairs

  • Corresponding angles — same position at each intersection.
  • Alternate interior — opposite sides of transversal, between the parallels.
  • Alternate exterior — opposite sides, outside the parallels.
  • Vertical angles at the same intersection.

Supplementary pair

Co-interior (same-side interior) angles sum to 180∘180^\circ.

Worked example

A transversal makes 120∘120^\circ with line A. The co-interior angle on line B (also parallel) is 180−120=60∘180 - 120 = 60^\circ. The corresponding angle on line B equals 120∘120^\circ.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

Corresponding angle to 75∘\text{Corresponding angle to } 75^\circ

Problem 2

Alternate interior to 60∘\text{Alternate interior to } 60^\circ

Problem 3

Co-interior to 110∘\text{Co-interior to } 110^\circ

Problem 4

Vertical to 50∘\text{Vertical to } 50^\circ

Practice

Standard problems matching the lesson.

Problem 5

Corresponding to 130∘\text{Corresponding to } 130^\circ

Problem 6

Alt interior to 45∘\text{Alt interior to } 45^\circ

Problem 7

Co-interior to 80∘\text{Co-interior to } 80^\circ

Problem 8

Alt exterior to 65∘\text{Alt exterior to } 65^\circ

Problem 9

Linear-pair partner of 70∘ on a line\text{Linear-pair partner of } 70^\circ \text{ on a line}

Problem 10

Co-interior: 4x and 2x+30. Find x.\text{Co-interior: } 4x \text{ and } 2x + 30. \text{ Find } x.

Problem 11

Corresponding: 3x=60. Find x.\text{Corresponding: } 3x = 60. \text{ Find } x.

Problem 12

Alt interior: 5x=80. Find x.\text{Alt interior: } 5x = 80. \text{ Find } x.

Problem 13

Transversal makes 105∘. Acute pair on other line?\text{Transversal makes } 105^\circ. \text{ Acute pair on other line?}

Problem 14

Corresponding to 35∘\text{Corresponding to } 35^\circ

Problem 15

Vertical to 110∘\text{Vertical to } 110^\circ

Problem 16

Co-interior to 110∘\text{Co-interior to } 110^\circ

Problem 17

Tracks make 50∘ with road. Corresponding on other track?\text{Tracks make } 50^\circ \text{ with road. Corresponding on other track?}

Problem 18

Sum of co-interior angles between parallels\text{Sum of co-interior angles between parallels}

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 19

Alt interior: 6x+10=4x+30. Find x.\text{Alt interior: } 6x + 10 = 4x + 30. \text{ Find } x.

Problem 20

Corresponding: 7x−5=4x+25. Find x.\text{Corresponding: } 7x - 5 = 4x + 25. \text{ Find } x.

Problem 21

Co-interior: 3x+(5x+20)=180. Find x.\text{Co-interior: } 3x + (5x + 20) = 180. \text{ Find } x.

Problem 22

Transversal makes 120∘. Supplement on same line?\text{Transversal makes } 120^\circ. \text{ Supplement on same line?}

Problem 23

Alt interior =72∘. Corresponding?\text{Alt interior } = 72^\circ. \text{ Corresponding?}

Problem 24

Linear pair to a corresponding angle of 135∘\text{Linear pair to a corresponding angle of } 135^\circ

Problem 25

Alt interior: 4x=80. Find x.\text{Alt interior: } 4x = 80. \text{ Find } x.

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