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Door 8 · Grade 7

📐 Angles in Parallel Lines & Triangles

Corresponding angles are EQUAL

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Parallel Lines Angle Relationships

When a transversal crosses two parallel lines, 8 angles are formed with special relationships:
Angle PairRelationshipExamplesCorrespondingEQUAL1=5, 2=6, 3=7, 4=8Alternate InteriorEQUAL3=6, 4=5Alternate ExteriorEQUAL1=8, 2=7Consecutive InteriorSum = 180 degrees3+5=180, 4+6=180Consecutive interior angles are also called co-interior or same-side interior angles.

Worked example

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

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

Answer: Angle 6 = 110 deg (consecutive interior: 70+110=180).

Triangle Angle Sum & Exterior Angle Theorem

Triangle Angle Sum Theorem: The three interior angles of any triangle always add up to 180 degrees.
Angle A + Angle B + Angle C = 180 degrees
Exterior Angle Theorem: An exterior angle of a triangle equals the sum of the two non-adjacent (remote) interior angles.
This is because the exterior angle and its adjacent interior angle form a straight line (180 deg), and that interior angle plus the other two = 180 deg.

Worked example

Problem: Triangle has angles 45 and 75 degrees. Find the third angle.

  1. Third angle = 180 - 45 - 75 = 60 degrees.

Answer: Third angle = 180 - 45 - 75 = 60 degrees.