Angles in Parallel Lines & Triangles • Topic 1 of 2

Parallel Lines Angle Relationships

When a transversal crosses two parallel lines, 8 angles are formed with special relationships:

Angle Pair	Relationship	Examples
Corresponding	EQUAL	1=5, 2=6, 3=7, 4=8
Alternate Interior	EQUAL	3=6, 4=5
Alternate Exterior	EQUAL	1=8, 2=7
Consecutive Interior	Sum = 180 degrees	3+5=180, 4+6=180

Consecutive interior angles are also called co-interior or same-side interior angles.

PARALLEL LINES WITH TRANSVERSAL:

     1 | 2
    ---|---  L1
     3 | 4

     5 | 6
    ---|---  L2
     7 | 8

Corresponding (equal): 1=5, 2=6, 3=7, 4=8
Alternate interior (equal): 3=6, 4=5
Alternate exterior (equal): 1=8, 2=7
Consecutive interior (sum 180): 3+5=180, 4+6=180

Solved Examples

Worked Example

If angle 1 = 70 degrees, find angles 5, 3, and 6.

SolutionAngle 5 = 70 deg (corresponding). Angle 3 = 70 deg (vertical to angle 1). Angle 6 = 110 deg (consecutive interior: 70+110=180).

Worked Example

Alternate interior angles are (3x+20) and (5x-40) degrees. Find x.

SolutionAlternate interior angles are equal: 3x+20 = 5x-40 => 60 = 2x => x = 30.

Key Points

Corresponding angles are EQUAL
Alternate interior angles are EQUAL
Alternate exterior angles are EQUAL
Consecutive interior angles SUM to 180 degrees

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.When a transversal cuts parallel lines, corresponding angles are:

Explanation: Corresponding angles are equal.

Q2.Alternate interior angles are:

Explanation: Equal.

Q3.Co-interior (allied) angles sum to:

Explanation: $180^\circ$.

Q4.A line that crosses two or more lines is a:

Explanation: Transversal.

Practice more MCQs → 📝 Assignment · 35 marks