Mathematics • Year 8 • Unit 3 • Lesson 14
Angles in Parallel Lines
Build fluency with the three parallel-line angle rules: corresponding (F) are equal, alternate (Z) are equal, co-interior (C) add to 180°.
1. I do, fully worked example
Three rules, three shapes: F (corresponding = equal), Z (alternate = equal), C (co-interior = 180°). Every answer needs a REASON.
Problem. Two parallel lines are cut by a transversal. One angle is 65°. Find the values of the corresponding, alternate, and co-interior angles to it.
Step 1, Identify each angle pair by SHAPE.
Corresponding (F): same position at each intersection. Alternate (Z): opposite sides of the transversal, between the parallels. Co-interior (C): same side of the transversal, between the parallels.
Step 2, Apply each rule.
Corresponding angle = 65° (corresponding angles, parallel lines)
Alternate angle = 65° (alternate angles, parallel lines)
Co-interior angle = 180° − 65° = 115° (co-interior, parallel lines)
Reason: ALWAYS write the reason next to the answer. "Corresponding angles, parallel lines" is the full reason, not just "F-shape".
Answer: Corresponding = 65°, Alternate = 65°, Co-interior = 115°.
2. We do, fill in the missing steps
Two parallel lines cut by a transversal. One angle is 110°. Fill in each blank. 4 marks
Step 1, Corresponding angle:
Corresponding angle = ______ ° (because corresponding angles are ____________ when lines are parallel)
Step 2, Alternate angle:
Alternate angle = ______ ° (because alternate angles are ____________ when lines are parallel)
Step 3, Co-interior angle:
Co-interior angle = 180° − ______ = ______ ° (because co-interior angles ____________)
Step 4, Vertically opposite angle (to the original 110°):
Vertically opposite = ______ °
3. You do, independent practice
Show all working AND the reason for every angle (just a number is worth zero marks). Foundation: name the rule. Standard: find the angle. Extension: algebra.
Foundation, identify and apply the rule
3.1 Two parallel lines are cut by a transversal. One angle is 72°. Find the corresponding angle. 1 mark
3.2 One angle is 48°. Find the alternate angle. 1 mark
3.3 One co-interior angle is 130°. Find the other co-interior angle. 1 mark
3.4 One angle at the intersection of a transversal with a parallel line is 85°. Find ALL eight angles formed when the same transversal crosses both parallel lines. 2 marks
Standard, find the unknown
3.5 Corresponding angles are 3x° and 75°. Find x. 2 marks
3.6 Co-interior angles are (x + 30)° and (2x + 60)°. Find x and both angles. 2 marks
Extension, algebraic alternate angles
3.7 Alternate angles are (3x − 10)° and (x + 30)°. Find x and both angles. 2 marks
3.8 Corresponding angles are (4x − 20)° and (2x + 40)°. Find x and the size of each angle. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2, We do (110° at one intersection)
Step 1: Corresponding = 110° (because corresponding angles are equal).
Step 2: Alternate = 110° (because alternate angles are equal).
Step 3: Co-interior = 180° − 110 = 70° (because co-interior angles add to 180°).
Step 4: Vertically opposite = 110°.
3.1, Corresponding to 72°
72° (corresponding angles, parallel lines).
3.2, Alternate to 48°
48° (alternate angles, parallel lines).
3.3, Co-interior to 130°
180° − 130° = 50° (co-interior angles, parallel lines).
3.4, All 8 angles when one is 85°
There are only TWO distinct angle values: 85° (×4) and 180° − 85° = 95° (×4). Pattern: at each intersection two angles are 85° and two are 95°; vertically opposite angles match.
3.5, Corresponding 3x° and 75°
Corresponding angles are equal: 3x = 75, so x = 25.
3.6, Co-interior (x+30)° and (2x+60)°
(x + 30) + (2x + 60) = 180 → 3x + 90 = 180 → 3x = 90 → x = 30. Angles: 60° and 120°.
3.7, Alternate (3x−10)° and (x+30)°
Alternate angles are equal: 3x − 10 = x + 30 → 2x = 40 → x = 20. Each angle = 3(20) − 10 = 50° (and (20)+30 = 50° ✓).
3.8, Corresponding (4x−20)° and (2x+40)°
4x − 20 = 2x + 40 → 2x = 60 → x = 30. Each angle = 4(30) − 20 = 100° (and 2(30)+40 = 100° ✓).