Angles and Equations Worksheet
Part 1 • 30 Min Algebraic Foundations
Name:
Date:
Period:
Two-Step Equations Mastery
Isolate the variable by using inverse operations in reverse order of operations (undo addition/subtraction, then multiplication/division).
Goal Show All Inverse Steps
1
Step 1: Undo Constant Term
Add or subtract the constant term on both sides.
→
2
Step 2: Undo Coefficient
Multiply or divide by the variable's coefficient.
→
✓
Step 3: Check
Substitute answer back into original equation.
Section A: Fundamental Two-Step Equations
Show both inverse operations
\(3x + 7 = 28\)
Workspace
\(x =\)
\(\frac{m}{4} - 5 = 3\)
Workspace
\(m =\)
\(-6y + 14 = -22\)
Workspace
\(y =\)
\(9 - 2k = 25\)
Workspace
\(k =\)
Section B: Rational Numbers & Grouped Terms
Clear fractions or distribute first
\(\frac{2}{3}p + 8 = 18\)
Workspace
\(p =\)
\(\frac{w - 7}{3} = 6\)
Workspace
\(w =\)
\(-4(n + 3) = 28\)
Workspace
\(n =\)
\(1.5a - 4.2 = 4.8\)
Workspace
\(a =\)
Section C: Real-World Modeling
Write an equation, then solve
- Carnival Ride Passes
Admission to a carnival is $15. Each ride ticket costs $3.50. Marcus spent $43 in total. How many tickets (\(t\)) did he buy?
Equation:
Solution: \(t =\) tickets
- Repair Service Fee
A plumber charges a flat call-out fee of $65 plus $45 per hour of work. A homeowner receives a bill for $245. How many hours (\(h\)) did the plumber work?
Equation:
Solution: \(h =\) hours
Part 1 Score: _____ / 10 Points Turn page for Part 2: Angle Relationships → Page 1 of 2
Part 2 • 30 Min Geometric Relationships
Student:
Period:
Complementary & Supplementary Angles
Use angle definitions to write equations, solve for unknown values (\(x\)), and calculate missing angle measures.
Key Rule Define • Equation • Solve
Complementary Angles
Sum to \(90^\circ\) (Right Angle)
\(\angle A + \angle B = 90^\circ\) • Look for square symbol \(\llcorner\)
Supplementary Angles
Sum to \(180^\circ\) (Linear Pair)
\(\angle 1 + \angle 2 = 180^\circ\) • Look for straight line
Section A: Diagram Setups & Unknowns
State relationship, write equation, solve
x 38°
Type: Complementary
Equation:
Find unknown angle: \(x =\) °
114° y
Type: Supplementary
Equation:
Find unknown angle: \(y =\) °
3x+6 48°
Write & Solve for \(x\):
Value of \(x\): \(x =\)
4x-10 70°
Write & Solve for \(x\):
Value of \(x\): \(x =\)
Section B: Algebraic Angle Systems
Find \(x\), then calculate both angle measures
- Complementary Pair
\(\angle A\) and \(\angle B\) are complementary. \(\text{m}\angle A = (5x + 4)^\circ\) and \(\text{m}\angle B = (2x + 2)^\circ\).
Equation:
\(x =\)
\(\text{m}\angle A =\) °
\(\text{m}\angle B =\) °
- Linear Pair (Supplementary)
\(\angle P\) and \(\angle Q\) form a straight line. \(\text{m}\angle P = (3x + 25)^\circ\) and \(\text{m}\angle Q = (x + 15)^\circ\).
Equation:
\(x =\)
\(\text{m}\angle P =\) °
\(\text{m}\angle Q =\) °
- Error Analysis & Synthesis Challenge
Critique & Correct
Jordan was asked to solve for \(x\) in two supplementary angles measuring \((6x - 4)^\circ\) and \(46^\circ\). Jordan wrote: \(6x - 4 + 46 = 90\) and concluded that \(x = 8\).
Explain Jordan's error:
Provide the correct equation and solution:
Correct Equation:
Correct \(x\): \(x =\)
Part 2 Score: _____ / 10 Points Total Practice Score: _____ / 20 Points Page 2 of 2
