Angle Relationships Practice Worksheet
Geometry SPED • Guided Practice
Angle Relationships Master Sheet
Name:
Date: Period:
Complementary
Angles that add to 90° (Corner)
\(\angle A + \angle B = 90^\circ\)
Supplementary
Angles that add to 180° (Straight line)
\(\angle 1 + \angle 2 = 180^\circ\)
Vertical Angles
Across the "X" • Always EQUAL
\(\angle \text{Top} = \angle \text{Bottom}\)
Part 1
Find the Missing Angle (Numeric Practice)
Problem 1 Complementary
38° a°
Equation: \(a + 38 = 90\)
Answer: \(a = \quad\quad^\circ\)
Problem 2 Linear Pair
115° b°
Equation: \(b + 115 = 180\)
Answer: \(b = \quad\quad^\circ\)
Problem 3 Vertical Angles
64° c° d°
Rule: Opposite angles are equal
Answer:
\(c = \quad^\circ\) \(d = \quad^\circ\)
Part 2
Guided Algebraic Angle Problem
Problem 4: Complementary Angles with Algebra
In the diagram, \(\angle A\) and \(\angle B\) form a right angle (\(90^\circ\)). Given that \(m\angle A = (3x + 3)^\circ\) and \(m\angle B = (5x + 7)^\circ\), find the value of \(x\) and the measure of each angle.
(5x+7)° (3x+3)° Q
Step 1: Relationship
What is the angle relationship?
Complementary (90°)
Supplementary (180°)
Vertical (Equal)
Step 2: Set Up Equation
Add expressions to equal 90°:
(3x + 3) + (5x + 7) = 90
Combine like terms:
Step 3: Solve for x
\(x = \quad\quad\)
Step 4: Find Angle Measures
\(m\angle A = 3( \quad ) + 3\)
\(= \quad\quad^\circ\)
\(m\angle B = 5( \quad ) + 7\)
\(= \quad\quad^\circ\)
Remember: Always check if the angle forms a corner (90°), a straight line (180°), or an "X" (Equal).
Geometry SPED • Advanced Practice
Solving for Unknowns & Linear Pairs
Page 2 of 2
Problem 5
Vertical Angles & Linear Pair Combo
Standard 1.14 Review
Look closely at the intersecting lines below:
1. Find the value of \(x\) using vertical angles.
2. Find the value of \(y\) using a linear pair.
3. Calculate the sum: \(x + y\).
(2x + 25)° y° (3x − 10)°
Part A: Solve for \(x\)
Relationship: Vertical Angles (=)
3x − 10 = 2x + 25
\(x = \quad\quad\)
Part B: Solve for \(y\)
Relationship: Linear Pair (180°)
First find top-left angle: \(2(\quad) + 25 =\)
\(y = \quad\quad^\circ\)
Part C: Sum of \(x + y\)
Add your two answers:
\(x + y = (\quad) + (\quad)\)
Sum =
Problem 6
Multi-Angle Identification
Lines intersect at point G
Three lines intersect at center point \(G\). Use angle relationships to determine the measure of each angle:
a. \(m\angle 1\) (Vertical to 50°):
Measure: ___°
b. \(m\angle 2\) (Vertical to 22°):
Measure: ___°
c. \(m\angle 3\) (Straight line = 180°):
Measure: ___°
d. \(m\angle 4\) (Vertical to \(\angle 3\)):
Measure: ___°
G 50° 22° ∠1 ∠2 ∠3 ∠4
Problem 7
Real-World Application: The Pizza Slice Cut
David is slicing a pizza. Two adjacent slices, \(\angle JKM\) and \(\angle MKL\), form a quarter-circle right angle (\(90^\circ\)).
If \(m\angle JKM = (2x + 10)^\circ\) and \(m\angle MKL = (4x + 20)^\circ\), what is the measure of \(m\angle JKM\)?
Equation & Solution:
(2x + 10) + (4x + 20) = 90
Value of \(x\): \(x = \quad\)
\(m\angle JKM\): \(\quad\quad^\circ\)
Self-Check: How confident do you feel about these angle relationships?
Got it! (Ready to test) Getting there (Need 1 more) Need Help
Angle Relationships Answer Key
Teacher Answer Key & Facilitation Geometry 1.14
Angle Relationships Key • Page 1
TEACHER COPY
Page 1 Solutions & Tips
SPED Memory Cues & Vocabulary Bridges
"C" is for Corner (90°):
Complementary starts with C. Turn the C into an 8 or 9 → 90° right angle.
"S" is for Straight (180°):
Supplementary starts with S. Straight line forms a flat 180° angle.
"V" in Vertical = "X":
Vertical angles look right across the X node. They are identical twins: Equal.
Part 1 Solutions
Problems 1–3 Worked Answers
Problem 1 Complementary
\(a + 38^\circ = 90^\circ\)
\(a = 90 - 38\)
\(a = 52^\circ\)
Common Error: Student subtracts from 180° instead of 90°. Remind them of the corner box!
Problem 2 Linear Pair
\(b + 115^\circ = 180^\circ\)
\(b = 180 - 115\)
\(b = 65^\circ\)
Check: Angle \(b\) is acute (<90°), matching the visual diagram.
Problem 3 Vertical Angles
\(c\) is vertical to \(64^\circ \implies \mathbf{c = 64^\circ}\)
\(d = 180 - 64 \implies \mathbf{d = 116^\circ}\)
\(c = 64^\circ, \; d = 116^\circ\)
Check: Total around circle = \(64+64+116+116 = 360^\circ\).
Part 2 Solution
Problem 4: Guided 4-Step Solution
Complementary Algebra
Step 1: Relationship
✓ Complementary (90°)
Supplementary
Vertical
Right angle box shows sum = 90°.
Step 2: Equation
(3x + 3) + (5x + 7) = 90
Combine like terms:
8x + 10 = 90
Add x terms: 3x + 5x = 8x
Add constants: 3 + 7 = 10
Step 3: Solve for x
8x + 10 = 90
− 10 − 10
8x = 80
x = 80 ÷ 8
x = 10
Remind students: x is not the angle measure yet!
Step 4: Angle Measures
\(m\angle A = 3(10) + 3\)
\(m\angle A = 33^\circ\)
\(m\angle B = 5(10) + 7\)
\(m\angle B = 57^\circ\)
Check: 33° + 57° = 90° ✓
Geometry Grade 10 SPED • Standard 1.14 Answer Key Continue to Page 2 for Advanced Problems 5–7 →
