Angle Hunter Worksheet
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Angle Hunter Worksheet
Transversals • Exterior Angles • AA Triangle Similarity
Grade 8 Geometry
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Quick Clue Toolkit • 3 Rules to Remember
1. Transversal Lines Parallel \(m \parallel n\)
• Corresponding: Equal (\(\angle 1 = \angle 5\))
• Alt. Interior: Equal (\(\angle 3 = \angle 6\))
• Same-Side Int.: Add to \(180^\circ\)
∠1 ∠3 ∠5 ∠6
2. Exterior Angle Rule Triangles
The outside angle equals the sum of the two remote (opposite) inside angles:
\(\text{Exterior } \angle = \angle a + \angle b\)
a b Ext ∠
3. AA Similarity \(\triangle \sim \triangle\)
If two angles of one triangle match two angles of another triangle, they are similar (same shape, different size).
40° 60° ~ 40° 60°
Level 1 • Guided Angle Investigations
Follow the clues and sentence frames to complete each step.
Scaffolded Practice
1 Transversal Angles: Lines \(L_1 \parallel L_2\).
The measure of \(\angle 1\) is \(120^\circ\). Find the measures of \(\angle 2\) and \(\angle 3\).
• \(\angle 1\) and \(\angle 2\) are in matching spots: corresponding angles. \(\text{m}\angle 2 =\) \(^\circ\)
• \(\angle 1\) and \(\angle 3\) are same-side interior (add to \(180^\circ\)):
\(180^\circ - 120^\circ =\) \(^\circ\) | \(\text{m}\angle 3 =\) \(^\circ\)
L₁ L₂ 120° (∠1) ∠2 ∠3
2 Exterior Angle: Find missing exterior angle \(x\).
In \(\triangle ABC\), the remote interior angles measure \(55^\circ\) and \(65^\circ\).
• Set up formula: \(x =\) \(^\circ\) \(+\) \(^\circ\)
Final Answer: \(x =\) \(^\circ\)
55° 65° x A B C
3 AA Similarity: Are \(\triangle JKL\) and \(\triangle MNP\) similar?
Find the 3rd angle of \(\triangle JKL\) to check if two angles match.
Missing \(\angle\) in \(\triangle JKL\): \(180^\circ - (45^\circ + 80^\circ) =\) \(^\circ\)
Do both triangles share 2 matching angles?
YES NO
Are the triangles similar (\(\sim\)) by AA?
YES NO
45° 80° △JKL 80° 55° △MNP
Angle Hunter Worksheet • Core Concepts & Supported Practice Page 1 of 2
Angle Hunter: Independent Mission
Part 2 • Independent Practice & Level Up Extension
Student Name:
Level 2 • Independent Practice
Apply your angle rules. Show all calculations in the workspace provided.
Core Mastery
4 Find the Missing Interior Angle:
The exterior angle of \(\triangle PQR\) is \(130^\circ\). One remote interior angle is \(52^\circ\). Find the value of \(y\).
Show equation and work:
Answer: \(y =\) \(^\circ\)
52° y 130° P Q R
5 Transversal Algebra: Parallel lines cut by transversal \(t\).
Alternate interior angles are equal: \(2x + 10 = 70\). Solve for \(x\).
Solve the 2-step equation:
Answer: \(x =\)
70° 2x + 10°
6 Bowtie Similarity: Segment \(AB \parallel CD\).
Explain why \(\triangle ABE \sim \triangle CDE\) using the Angle-Angle (AA) rule.
1st Pair: \(\angle AEB\) and \(\angle CED\) match because they are angles.
2nd Pair: \(\angle A\) and \(\angle D\) match because they are alternate angles.
Are \(\triangle ABE\) and \(\triangle CDE\) similar by AA?
YES NO
A B C D E
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Level 3 • "Level Up" Extension Challenge
All-In-One Puzzle
An architect designs a ramp frame where horizontal beams are parallel (\(H_1 \parallel H_2\)).
Part A (Alt. Interior): Find angle \(a\):
\(a =\) \(^\circ\)
Part B (Exterior Angle Theorem):
The triangle has remote angles \(a\) and \(50^\circ\). Find \(z\):
\(z =\) \(^\circ\)
Part C (Bonus): Why are triangles similar? Because they share
H₁ H₂ 35° a 50° z
Angle Hunter Worksheet • Independent Practice & Level Up Extension Page 2 of 2
