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 complementary, supplementary, vertical, and adjacent angles from diagrams with at least 80% accuracy.
- Determine the measure of an unknown angle when given a complementary or supplementary angle, demonstrating the correct calculation in at least 4 out of 5 problems.
- Explain the relationship between vertical angles and congruent angles in their own words, providing at least two accurate examples.
- Apply knowledge of angle relationships to solve for unknown angle measures in complex diagrams containing multiple types of angles, achieving a score of 70% or higher on a problem set.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define complementary, supplementary, vertical, adjacent, and congruent angles.
Identify pairs of special angles in complex diagrams involving intersecting lines.
Calculate the measure of an unknown angle using the properties of these angle relationships.
Set up and solve algebraic equations involving angle relationships.
Differentiate between adjacent angles and linear pairs.
Apply the Vertical Angles Theorem as a justification in geometric reasoning.
Ever notice how the intersecting lines of a city map, a scissor's blades, or a building's frame create specific, predictable angles? 🗺️ Let's decode the geometry hidden in plain sight!
This tutorial is your foundation for understanding the relationships between angles. Mastering these concept...
2
Key Concepts & Vocabulary
TermDefinitionExample
Adjacent AnglesTwo angles that share a common vertex and a common side, but do not have any 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.
Vertical AnglesA pair of opposite angles made by two intersecting lines. They are always congruent (equal in measure).When two straight roads cross, the angle of the northeast corner is a vertical angle to the southwest corner.
Complementary AnglesTwo angles whose measures add up to 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 add up to 180 degrees. If they are adjacent, they form a st...
3
Core Formulas
Complementary Angles Sum
If ∠A and ∠B are complementary, then m∠A + m∠B = 90°
Use this rule when you know two angles form a right angle. If you know one angle, you can find the other by subtracting its measure from 90°.
Supplementary Angles Sum
If ∠A and ∠B are supplementary, then m∠A + m∠B = 180°
Use this rule when two angles form a straight line (a linear pair) or are otherwise stated to be supplementary. If you know one angle, you can find the other by subtracting its measure from 180°.
Vertical Angles Theorem
If ∠A and ∠B are vertical angles, then m∠A = m∠B (or ∠A ≅ ∠B)
This is a powerful theorem for proofs and problem-solving. When you see two intersecting lines, you immediately know the opposite angles are equal.
4 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
A student makes the following claim: 'If two angles are adjacent, they must be supplementary.' Which of the following diagrams provides a counterexample to this claim?
A.diagram of two intersecting lines, showing a pair of adjacent angles that form a straight line.
B.diagram of a 90° angle divided into two smaller adjacent angles of 30° and 60°.
C.diagram showing two non-adjacent 90° angles.
D.diagram showing two vertical angles, each measuring 120°.
Challenging
The measure of the supplement of an angle is five times the measure of its complement. What is the measure of the angle?
A.22.5°
B.30°
C.67.5°
D.60°
Challenging
In the figure, lines l and m intersect at point P, and line n intersects line m at point Q. Given m∠1 = (3x + y)°, m∠2 = 95°, m∠3 = (2x + y)°, and m∠5 = 125°. Find the value of x.
A.15
B.20
C.25
D.30
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing FreeMore from Congruent triangles
Mathematics for other grades
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 complementary, supplementary, vertical, and adjacent angles from diagrams with at least 80% accuracy; Determine the measure of an unknown angle when given a complementary or supplementary angle, demonstrating the….
Is "Identify complementary, supplementary, vertical, adjacent, and congruent 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 Identify complementary, supplementary, vertical, adjacent, and congruent angles?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.