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Algebraic Equations
Setting up and Solving Equations for Basic Geometric Relationships
The ConceptThis Checkpoint requires students to be
proficient on multiple previous Checkpoints.
If you are having trouble with any of those concepts, please view those particular tutorials.
The Concept1. For Each Question The First Thing You Must
Do Is Identify The Relationship.2. The Next Step Is To Use The Relationship To
Setup An Equation.3. Solve The Equation4. Use The Answer To Complete The Problem.
Example 1
Identify the relationship: “Triangle Sum Theorem”- The 3 angles of a triangle have a sum of 180°
5x + 12°
3x - 20° 2x - 22°
What is the measure of Angle A?
A
B C
Example 1
Setup an Equation: (5x + 12) + (3x – 20) + (2x – 22) = 180°
5x + 12°
3x - 20° 2x - 22°
What is the measure of Angle A?
A
B C
Example 1
Solve the Equation: (5x + 12) + (3x – 20) + (2x – 22) = 180°
10x – 30 = 180° 10x = 210°
x = 21°
5x + 12°
3x - 20° 2x - 22°
What is the measure of Angle A?
A
B C
Example 1
Use The Answer To Complete The Problem SINCE x = 21°, then Angle A = 5x + 12°Angle A = 5(21°) + 12°Angle A = 105° + 12°Angle A = 117°
5x + 12°
3x - 20° 2x - 22°
What is the measure of Angle A?
A
B C
Example 2
Identify the relationship: B & C are not relatedHowever, Angles A & C are corresponding angles and therefore are equalAND A & B are a straight angle pair and therefore have a sum of 180°
5x - 30°
3x + 10° What is the measure of Angle A?
B
C
A
Example 2
Setup an Equation: m<A + m<B = 180°m<A = m<Cm<C + m<B = 180°(3x + 10°) + (5x - 30°) = 180°
5x - 30°
3x + 10° What is the measure of Angle A?
B
C
A
Example 2
Solve the Equation: (3x + 10°) + (5x - 30°) = 180°
8x - 20° = 180° 8x = 200° x = 25°
5x - 30°
3x + 10° What is the measure of Angle A?
B
C
A
Example 2
Use The Answer To Complete The Problem x = 25°m<A = m<C = 5x - 30°m<A = 5(25°) - 30°m<A = 125°- 30° = 95°
5x - 30°
3x + 10° What is the measure of Angle A?
B
C
A
