a = b | Same side of transversal Ā· Equal Look for the F or its mirror image
Alternate Angles (Z-shape)
a = b | Opposite sides of transversal Ā· Equal Look for the Z or its mirror image
Co-interior Angles (C-shape)
a + b = 180Ā° | Same side Ā· Supplementary Also called allied or same-side interior angles
Vertically Opposite
a = b | Formed by crossing lines Ā· Equal Always state the reason in your working
Quick rules at a glance š
F-shape F Corresponding = equal
Z-shape Z Alternate = equal
C-shape C Co-interior = 180Ā°
X-cross ā Vert. opp. = equal
What you'll learn:
The 5 key angle rules for parallel lines
How to identify F, Z, C and X patterns in diagrams
How to find unknown angles ā always with a reason
Combining multiple rules in multi-step problems
Interactive diagram: drag the transversal and watch all 8 angles update live
Games: Name That Rule, Multi-Step Builder, Angle Hunt
š Learn: Angles in Parallel Lines
Part 1: Corresponding Angles (F-shape) š
Corresponding
When a transversal crosses two parallel lines it creates pairs of corresponding angles. They sit on the same side of the transversal ā one at the top parallel line, one at the bottom ā and they are always equal.
They form an F-shape (or a back-to-front F). The two highlighted angles are in the same position at each intersection.
š” Reason to write: "Corresponding angles ā parallel lines"
Part 2: Alternate Angles (Z-shape) šµ
Alternate
Alternate angles are on opposite sides of the transversal, between the two parallel lines. They are always equal.
They form a Z-shape (or back-to-front Z / S-shape). The angles are tucked inside the parallel lines.
š” Reason to write: "Alternate angles ā parallel lines"
Part 3: Co-interior Angles (C-shape) š¢
Co-interior
Co-interior angles (also called allied or same-side interior angles) are on the same side of the transversal, between the parallel lines. They always add up to 180Ā°.
They form a C-shape (or back-to-front C). Think: "C for Co-interior, they are Complementary to a straight line".
š” Reason to write: "Co-interior angles ā parallel lines (sum to 180Ā°)"
Part 4: Vertically Opposite Angles š£
Vertically Opposite
When two straight lines cross, the angles directly opposite each other at the point of intersection are equal. This rule applies at any crossing ā not just parallel lines.
š” Reason to write: "Vertically opposite angles"
Part 5: Angles on a Straight Line š“
Straight Line
All angles on a straight line add up to 180Ā°. This is a foundational rule used in almost every multi-step problem ā use it to find missing angles at an intersection.
š” Reason to write: "Angles on a straight line sum to 180Ā°"
š” Worked Examples
Example 1 ā Corresponding Angles
Find angle a. Lines are parallel.
Step 1: The marked angle 65Ā° and a are corresponding angles (F-shape).
Step 2: Corresponding angles are equal when lines are parallel.
a = 65Ā° (corresponding angles ā parallel lines)
Example 2 ā Alternate Angles
Find angle b. Lines are parallel.
Step 1: 48Ā° and b are on opposite sides of the transversal, between the parallel lines ā alternate angles (Z-shape).
b = 48Ā° (alternate angles ā parallel lines)
Example 3 ā Co-interior Angles
Find angle c. Lines are parallel.
Step 1: Both angles are between the parallel lines on the left side of the transversal ā co-interior angles (C-shape).
Step 2: Co-interior angles add up to 180Ā°.
c + 110Ā° = 180Ā°
c = 70Ā° (co-interior angles ā parallel lines ā sum to 180Ā°)
Example 4 ā Multi-step Problem
Lines p and q are parallel. The transversal makes an angle of 72Ā° with line p. Find angles x and y, giving reasons.
Step 1: Find x using corresponding angles: x = 72Ā° (corresponding angles, p ā„ q)
Step 2: Find y using co-interior angles: y + 72Ā° = 180Ā°, so y = 108Ā° (co-interior angles, p ā„ q)
Check: x + y = 72Ā° + 108Ā° = 180Ā° ā (angles on a straight line)
x = 72Ā°, y = 108Ā°
š Interactive Parallel Lines Visualizer
Drag the slider to change the transversal angle. Click any angle sector to highlight its partner and see the relationship!
Corresponding (F)
Alternate (Z)
Co-interior (C)
Vertically Opposite
Transversal angle: 55Ā°
Click any angle sector above to see its partner highlighted and read the angle rule.
š® Name That Rule Game
Score: 0 / 0
Two angles are highlighted. Which rule connects them?
š§± Multi-Step Angle Builder
A diagram has a transversal cutting two parallel lines. You are given angle A = 73Ā° at the top intersection. Use the dropdowns to find the remaining angles step by step.
Find angle B (top intersection, other side of transversal):
Find angle C (bottom intersection, corresponding to A):
Find angle D (bottom intersection, co-interior with A):
š Angle Hunt
The marked angle (orange) is 65Ā°. Click all sectors in the diagram that are equal to it. Watch out ā some are NOT equal!
Click the sectors that equal the orange angle.
āļø Exercise 1: Corresponding Angles
Find each unknown angle. Lines marked ā„ are parallel. Always state the rule.
āļø Exercise 2: Alternate Angles
Find each unknown angle. Lines marked ā„ are parallel. Always state the rule.
āļø Exercise 3: Co-interior Angles
Find each unknown angle. Lines are parallel. Show your working.
āļø Exercise 4: Mixed Rules ā Find the Angle
Lines are parallel. Use the correct rule for each. Enter the angle value.
š Exercise 5: Multi-step Problems
Each question requires two or more steps. Select the correct rule from the dropdown, then type the angle.
š Practice ā 20 Questions
Click the correct rule or angle value for each question.
š Challenge ā 8 Hard Questions
Multi-step, worded, and proof-style questions. Show all reasoning.