Angle Addition Practice Worksheet
Geometry 1.12 SPED Scaffolded Review
Angle Addition Postulate: Part + Part = Whole
Name:
Date: Period:
V Part 2 Part 1
Visual Rule
Angle 1 (Part) + Angle 2 (Part) = Total Angle (Whole)
STEP 1 Identify Parts
STEP 2 Write Equation
STEP 3 Solve for \(x\)
STEP 4 Find Target \(\angle\)
LEVEL 1 Supported Practice (Guided Problem Steps)
#1) Guided Model
In the diagram, ray \(UY\) is inside \(\angle XUZ\). If \(m\angle XUY = (6x + 3)^\circ\), \(m\angle YUZ = (3x - 4)^\circ\), and the total angle is \(m\angle XUZ = 98^\circ\), what is the value of \(m\angle XUY\)?
Z Y X U 3x - 4 6x + 3 Whole = 98°
Step 1: Identify
Part 1 = 6x + 3
Part 2 = 3x - 4
Whole = 98°
Part + Part = Whole
Step 2: Set Up
(6x + 3) + (3x - 4) = 98
Combine like terms:
9x - 1 = 98
Step 3: Solve for \(x\)
9x = 98 + 1
9x = 99
x = 11
Divide by 9
Step 4: Answer
Find \(m\angle XUY = 6x + 3\):
\(6(11) + 3 = 69^\circ\)
\(m\angle XUY = 69^\circ\)
#2) Your Turn
In the diagram, ray \(DH\) divides \(\angle EDC\). Determine \(m\angle EDC\) if \(m\angle EDC = (8x - 6)^\circ\), \(m\angle EDH = 54^\circ\), and \(m\angle HDC = (x + 10)^\circ\).
E H C D 54° x + 10 Whole = 8x - 6
Step 1: Identify
Part 1:
Part 2:
Whole:
Label parts & whole
Step 2: Write Equation
Part + Part = Whole
Step 3: Solve for \(x\)
Show algebra steps:
\(x\) = _____
Step 4: Find \(m\angle EDC\)
Substitute \(x\) into expression:
\(m\angle EDC\) = _____°
Geometry 1.12 • Angle Addition Postulate • Review & Practice Page 1 of 2
Geometry 1.12
Tiered Mastery Practice
Student Name:
LEVEL 2 On-Level (Straight Angles & Angle Decompositions)
#3) Straight Angle = 180°
Line \(\overline{JM}\) forms a straight angle at vertex \(K\). If \(m\angle JKN = (4x + 10)^\circ\), \(m\angle NKL = (3x + 10)^\circ\), and \(m\angle LKM = (2x + 25)^\circ\):
K J M N L Total = 180°
a) Write Equation:
Angle 1 + Angle 2 + Angle 3 = 180°
b) Solve for \(x\):
\(x\) = _____
c) Find \(m\angle NKM\):
Hint: \(m\angle NKL + m\angle LKM\)
\(m\angle NKM\) = _____°
#4) Overlap Method
In the figure below, \(m\angle PQS = 86^\circ\), \(m\angle RQT = 74^\circ\), and their overlap is \(m\angle RQS = 48^\circ\). Find the total angle \(m\angle PQT\).
Q T S R P Overlap 48°
Part A: Left Piece
\(m\angle PQR = 86^\circ - 48^\circ\)
\(m\angle PQR\) = _____°
Part B: Right Piece
\(m\angle SQT = 74^\circ - 48^\circ\)
\(m\angle SQT\) = _____°
Total Angle \(m\angle PQT\)
Add Left + Middle + Right
\(m\angle PQT\) = _____°
LEVEL 3 #5) Quadratic Extension
In the figure below, \(m\angle CXE = 70^\circ\). If \(m\angle CXD = (x^2)^\circ\) and \(m\angle EXD = (3x)^\circ\), find the values of \(m\angle CXD\) and \(m\angle EXD\).
X E D C 3x x² Total = 70°
Step 1: Set to 0
x² + 3x = 70
x² + 3x - 70 = 0
Subtract 70 from both sides
Step 2: Factor
Find 2 numbers that multiply to -70 and add to 3:
(x + 10)(x - 7) = 0
\(x = 7\) (angle must be > 0)
Step 3: Calculate Angles
\(m\angle CXD = 7^2 =\) _____°
\(m\angle EXD = 3(7) =\) _____°
Check: Sum = 70°!
Geometry 1.12 • Angle Addition Postulate • Review & Practice Page 2 of 2
Angle Addition Exit Ticket
Exit Ticket Lesson 1.12 Check
Angle Addition Postulate Check
Name:
Date: Score: /10
Core Rule: Part 1 + Part 2 = Whole Angle
Show all work for full credit.
#1) Decomposition
In the diagram below:
• \(m\angle PQS = 87^\circ\)
• \(m\angle RQT = 72^\circ\)
• \(m\angle RQS = 50^\circ\) (middle overlap)
Find the measure of the total angle \(m\angle PQT\).
Q T S R P Overlap 50°
Step 1: Left Piece
\(m\angle PQR = 87^\circ - 50^\circ\)
\(m\angle PQR\) = _____°
Step 2: Right Piece
\(m\angle SQT = 72^\circ - 50^\circ\)
\(m\angle SQT\) = _____°
Step 3: Total Angle
Add Left + Middle + Right
\(m\angle PQT\) = _____°
#2) Algebra Application
Ray \(SJ\) divides \(\angle TSR\). Given:
• \(m\angle TSJ = (2x^2)^\circ\)
• \(m\angle JSR = (4x + 50)^\circ\)
• \(m\angle TSR = (13x + 55)^\circ\) (Total Angle)
Find the measure of \(m\angle JSR\).
S R J T 4x + 50 2x²
Step A: Set Equation = 0
2x² + 4x + 50 = 13x + 55
2x² - 9x - 5 = 0
Subtract 13x & 55 from both sides
Step B: Solve for \(x\)
Factoring scaffold:
(2x + 1)(x - 5) = 0
Choose positive length:
\(x\) = _____
Step C: Find \(m\angle JSR\)
Plug \(x\) into \(4x + 50\):
\(m\angle JSR\) = _____°
Student Reflection & Self-Assessment Circle or check your rating below
Got It!
I can solve Part + Part = Whole on my own
Almost There
I need help setting up or solving for \(x\)
Need Help
I'm still confused about identifying parts
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Geometry 1.12 • Angle Addition Postulate • Exit Ticket Formative Assessment
Angle Addition Teacher Guide
Teacher Reference Answer Key & Accommodations
Angle Addition Postulate: Teacher Guide
Course: 10th Grade Geometry (SPED)
Standard: GEO 1.12 Angle Addition
Targeted SPED Accommodations & Misconception Interventions
Misconception: Stopping after finding \(x\)
Students often feel relief upon finding \(x = 11\) and circle it. Teacher Prompt: "Great job finding \(x\)! Now reread the bold question: does it ask for \(x\) or for the angle?" Remind them of Step 4 (Substitute).
Misconception: Setting Parts Equal (\(\text{Part}_1 = \text{Part}_2\))
Students confuse angle bisectors with the Angle Addition Postulate. Teacher Prompt: "Are these two angles labeled identical? No! We must ADD them together to make the big angle."
Visual Scaffolding: Highlighting Rays
Have students physically use two highlighters: yellow for Part 1, pink for Part 2. The combined overlapping area at the vertex visually reinforces Part + Part = Total.
Algebra Support: Equation T-Charts
For students struggling with multi-step equations, provide a vertical line down the equals sign to balance operations (+1 on both sides, divide by coefficient).
SOLUTIONS Worksheet Page 1 (Level 1: Supported)
Problem #1: Model Guided Problem Answer: \(m\angle XUY = 69^\circ\)
Step 1: Identify
Part 1 = \(6x + 3\)
Part 2 = \(3x - 4\)
Whole = \(98^\circ\)
Step 2: Equation
\((6x + 3) + (3x - 4) = 98\)
9x - 1 = 98
Step 3: Solve
9x = 99
x = 11
Step 4: Substitute
\(6(11) + 3\)
\(m\angle XUY = 69^\circ\)
(\(m\angle YUZ = 29^\circ\); sum = \(98^\circ\))
Problem #2: Student Practice Answer: \(m\angle EDC = 74^\circ\)
Step 1: Identify
Part 1 (\(\angle EDH\)) = \(54^\circ\)
Part 2 (\(\angle HDC\)) = \(x + 10\)
Whole (\(\angle EDC\)) = \(8x - 6\)
Step 2: Equation
\(54 + (x + 10) = 8x - 6\)
x + 64 = 8x - 6
Step 3: Solve
64 + 6 = 8x - x
70 = 7x
x = 10
Step 4: Substitute
