Angle Navigator Reference Sheet
Angle Navigator
8th Grade Geometry Quick Reference Guide • Angle Rules & Lines
Name: Period:
Part 1
Two-Angle Relationships (Intersection & Lines)
Complementary
SUM = 90°
Two angles that combine to form a right angle (corner).
💡 Memory Clue: C is for Corner (90°)
38° x
Worked Example: x + 38° = 90°
1. Subtract known: 90 - 38
2. Solve: x = 52°
Supplementary
SUM = 180°
Two angles on a straight line that add to 180° (linear pair).
💡 Memory Clue: S is for Straight (180°)
125° y
Worked Example: y + 125° = 180°
1. Subtract known: 180 - 125
2. Solve: y = 55°
Vertical Angles
EQUAL (=)
Opposite angles formed by crossing lines. Always congruent!
💡 Memory Clue: X marks the spot; across are twins
68° a b b
Worked Example: a = 68°
1. Across from 68°: Direct match!
2. Answer: a = 68°
Part 2
Transversals & Parallel Lines (Line m ∥ Line n)
⚡ The Golden Secret: Only 2 angle measures exist! (All Acute Equal • All Obtuse Equal)
Line m Line n Transversal t 1 2 3 4 5 6 7 8
All Acute Angles Equal: ∠2 = ∠3 = ∠6 = ∠7 All Obtuse Angles Equal: ∠1 = ∠4 = ∠5 = ∠8
Corresponding EQUAL (=)
Matching position at each intersection ("slides over").
∠2 = ∠6 | ∠1 = ∠5
Alt. Interior EQUAL (=)
Inside parallel lines, on opposite sides of transversal ("Z shape").
∠3 = ∠6 | ∠4 = ∠5
Alt. Exterior EQUAL (=)
Outside parallel lines, on opposite sides of transversal.
∠1 = ∠8 | ∠2 = ∠7
Same-Side Interior SUM = 180°
Inside parallel lines, on the same side of transversal ("C shape").
∠3 + ∠5 = 180° | ∠4 + ∠6 = 180°
Golden Check: If angles look congruent (both acute or both obtuse), set them EQUAL. If one is acute and one is obtuse, set their SUM = 180°!
Page 1 of 2
Triangle Rules & Similarity
8th Grade Geometry Quick Reference Guide • Interior, Exterior & AA Theorem
TOOLKIT 2
Theorem 1
Triangle Angle Sum
Inside Sum = 180°
The three interior angles of any triangle always add up to exactly 180°.
∠A + ∠B + ∠C = 180°
Strategy: Add the 2 given angles together, then subtract from 180° to find the missing angle.
65° 45° x
Step-by-Step Solve:
Step 1: Add known angles:
65° + 45° = 110°
Step 2: Subtract from 180°:
180° - 110° = 70°
Answer: x = 70°
Theorem 2
Exterior Angle Theorem
Outside = Remote 1 + Remote 2
An exterior angle on an extended side equals the sum of the two remote (far-away) interior angles.
Exterior ∠d = Remote 1 + Remote 2
Bonus Check: The exterior angle and its next-door neighbor always form a straight line (180°)!
52° 64° d
Step-by-Step Solve:
Identify: Remote interior angles are 52° and 64°.
Calculate: Add remote angles:
d = 52° + 64° = 116°
Answer: d = 116°
Theorem 3
AA Triangle Similarity (Angle-Angle)
2 Angles Match = Similar (∼)
If TWO angles of one triangle are congruent to two angles of another triangle, the triangles are SIMILAR (same shape, proportional sides).
💡 Why only 2 angles? Because all 3 angles add to 180°, if 2 match, the 3rd angle must match automatically!
70° 50° 60° ΔABC ∼ 70° 50° 60° ΔDEF
AA Test:
• ∠A = ∠D = 70° ✓
• ∠B = ∠E = 50° ✓
ΔABC ∼ ΔDEF by AA
8th Grade Detective Guide: "What Rule Do I Use?"
Square Corner (∟)?
Angles make a right angle.
Set sum = 90°
Straight Line?
Angles lie flat along line.
Set sum = 180°
"X" Intersection?
Angles across from vertex.
Set angles EQUAL
Inside a Triangle?
All 3 interior corners.
Set sum = 180°
Always show your work: 1) Identify relationship, 2) Write the algebra equation, 3) Solve & check with mental math!
Page 2 of 2
