Mathematics
Grade 10
15 min
Find measures of complementary, supplementary, vertical, and adjacent angles
Find measures of complementary, supplementary, vertical, and adjacent angles
What you'll learn
- Identify the reciprocal of a given fraction or whole number with at least 80% accuracy.
- Explain in their own words why multiplying a number by its reciprocal equals 1, using examples.
- Solve division problems involving fractions by rewriting them as multiplication problems using reciprocals, achieving at least 70% accuracy on a worksheet.
- Apply the concept of reciprocals to solve real-world word problems involving dividing fractions, demonstrating understanding by correctly setting up and solving at least 2 out of 3 problems.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define and identify complementary, supplementary, vertical, and adjacent angles in a diagram.
Formulate algebraic equations based on the relationships between angle pairs.
Solve for unknown angle measures by applying the properties of complementary and supplementary angles.
Solve for unknown angle measures using the Vertical Angles Theorem.
Distinguish between adjacent angles and a linear pair.
Solve multi-step problems that combine multiple angle pair relationships.
Ever noticed how the streets on a city map intersect to form different angles? 🗺️ The relationships between those angles are critical for everything from navigation to architecture!
This tutorial will explore four fundamental angle relationships: complementary, supplementary, vertical, and a...
2
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 diagram where ray OB extends from the vertex O between the rays OA and OC, ∠AOB and ∠BOC are adjacent angles.
Complementary AnglesTwo angles whose measures have a sum of 90 degrees. They do not have to be adjacent.A 30° angle and a 60° angle are complementary because 30° + 60° = 90°.
Supplementary AnglesTwo angles whose measures have a sum of 180 degrees. They do not have to be adjacent.A 110° angle and a 70° angle are supplementary because 110° + 70° = 180°.
Linear PairA pair of adjacent angles whose non-common sides are opposite rays (form a straight line). Angles in a linear pair are always supplementary.If two an...
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Core Formulas
Complementary Angles Sum
If ∠A and ∠B are complementary, then m∠A + m∠B = 90°
Use this rule when you are given that two angles are complementary or when they form a right angle. Set the sum of their measures equal to 90 to find an unknown value.
Supplementary Angles Sum / Linear Pair Postulate
If ∠A and ∠B are supplementary, then m∠A + m∠B = 180°
Use this rule when you are told two angles are supplementary or when they form a linear pair (a straight line). Set the sum of their measures equal to 180.
Vertical Angles Theorem
If ∠A and ∠C are vertical angles, then m∠A = m∠C (or ∠A ≅ ∠C)
Use this theorem when you have two intersecting lines. Set the measures of the angles opposite each other at the intersection point equal to each other.
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Easy
Which of the following statements best defines supplementary angles?
A.Two angles whose measures sum to 90 degrees.
B.Two angles that are opposite each other when two lines intersect.
C.Two angles whose measures sum to 180 degrees.
D.Two angles that share a common vertex and a common side.
Easy
In a diagram where two lines intersect, what is the relationship between vertical angles?
A.They are always supplementary.
B.They are always complementary.
C.They are always congruent.
D.They are always adjacent.
Easy
If m∠A = 47°, what is the measure of the complement of ∠A?
A.43°
B.53°
C.133°
D.47°
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Frequently asked questions
What grade level is "Find measures of complementary, supplementary, vertical, and adjacent angles"?
Find measures of complementary, supplementary, vertical, and adjacent angles is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Find measures of complementary, supplementary, vertical, and adjacent angles?
You'll be able to: Identify the reciprocal of a given fraction or whole number with at least 80% accuracy; Explain in their own words why multiplying a number by its reciprocal equals 1, using examples; Solve division problems involving fractions….
Is "Find measures of complementary, supplementary, vertical, and adjacent angles" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Find measures of complementary, supplementary, vertical, and adjacent angles?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.