Mathematics
Grade 10
15 min
Identify complementary, supplementary, vertical, adjacent, and congruent angles
Identify complementary, supplementary, vertical, adjacent, and congruent angles
What you'll learn
- Identify and list at least three equivalent fractions for a given fraction, demonstrating understanding of how to multiply or divide the numerator and denominator by the same number.
- Solve at least 8 out of 10 addition and subtraction problems involving fractions with unlike denominators by finding a common denominator.
- Explain in writing or verbally how to compare two fractions with different numerators and denominators using benchmark fractions (0, 1/2, 1) or common denominators.
- Apply knowledge of fractions to solve 3 out of 4 word problems involving addition, subtraction, and comparison of fractions in real-world scenarios.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define complementary, supplementary, vertical, adjacent, and congruent angles.
Identify angle pairs in complex diagrams and geometric figures.
Differentiate between angle pairs that share characteristics, such as adjacent angles and linear pairs.
Set up and solve algebraic equations to find unknown angle measures using the properties of these angle relationships.
Apply the Vertical Angles Theorem and the Linear Pair Postulate as foundational steps in geometric reasoning.
Justify claims about angle measures in multi-step problems.
Ever wonder how city planners design perfect street intersections or how animators create realistic movements? 🗺️ It all starts with the fundamental relationships between angles!
This tutorial will equip you with the essential v...
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Key Concepts & Vocabulary
TermDefinitionExample
Adjacent AnglesTwo angles that share a common vertex and a common side, but have no common interior points. They are 'next to' each other.In a clock face, the angle formed by the hands at 12 and 1, and the angle formed by the hands at 1 and 2, are adjacent.
Complementary AnglesA pair of angles whose measures add up to 90 degrees. They do not have to be adjacent.An angle of 30° and an angle of 60° are complementary because 30 + 60 = 90.
Supplementary AnglesA pair of angles whose measures add up to 180 degrees. They do not have to be adjacent.An angle of 110° and an angle of 70° are supplementary because 110 + 70 = 180. A special case of adjacent supplementary angles is a 'linear pair'.
Vertical AnglesThe pair of opposite angles formed by two inters...
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Core Formulas
Complementary Angles Sum
m∠1 + m∠2 = 90°
Use this formula when you know two angles are complementary. If you know one angle, you can find the other. If angles are expressed with variables, you can set up an equation.
Supplementary Angles Sum / Linear Pair Postulate
m∠1 + m∠2 = 180°
Use this formula when two angles are supplementary or form a linear pair. This is fundamental for problems involving intersecting lines and is a key reason in geometric proofs.
Vertical Angles Theorem
If ∠1 and ∠3 are vertical angles, then m∠1 = m∠3.
Use this theorem to set the measures of two vertical angles equal to each other. This is often the first step in solving for variables in diagrams with intersecting lines.
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Challenging
In the figure, line AC is perpendicular to line BD at point O. Ray OE bisects ∠FOD. If m∠FOC = 120°, what is m∠AOE?
A.105°
B.120°
C.150°
D.135°
Challenging
The measure of the supplement of an angle is 20° more than three times the measure of its complement. Find the measure of the angle.
A.55°
B.35°
C.45°
D.65°
Challenging
Two lines intersect. The sum of the measures of one pair of vertical angles is 140°. What is the measure of one of the other angles?
A.40°
B.70°
C.110°
D.140°
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Frequently asked questions
What grade level is "Identify complementary, supplementary, vertical, adjacent, and congruent angles"?
Identify complementary, supplementary, vertical, adjacent, and congruent angles is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Identify complementary, supplementary, vertical, adjacent, and congruent angles?
You'll be able to: Identify and list at least three equivalent fractions for a given fraction, demonstrating understanding of how to multiply or divide the numerator and denominator by the same number; Solve at least 8 out of 10 addition and….
Is "Identify complementary, supplementary, vertical, adjacent, and congruent angles" free to practice?
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How many practice questions are included with Identify complementary, supplementary, vertical, adjacent, and congruent angles?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.