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 complementary, supplementary, vertical, and adjacent angles when presented in diagrams with at least 80% accuracy.
- Solve for unknown angle measures in complementary and supplementary angle problems, showing all work, with at least 70% accuracy.
- Apply the properties of vertical angles to determine unknown angle measures in diagrams, justifying each step with the correct angle relationship terminology, with at least 75% accuracy.
- Explain the relationship between adjacent angles that form a linear pair (supplementary angles) in their own words, demonstrating understanding in a written response of at least three sentences.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify complementary, supplementary, vertical, and adjacent angles in various geometric figures.
Formulate and solve algebraic equations to find unknown angle measures based on their relationships.
Apply the Vertical Angles Congruence Theorem to determine angle measures.
Use the Linear Pair Postulate to find the measure of a supplementary angle.
Differentiate between adjacent angles and a linear pair.
Apply knowledge of angle relationships as a foundational step in geometric proofs, particularly for congruent triangles.
Ever wonder how architects ensure corners are perfectly square and how city planners design intersections that work? 📐 It all comes down to the fundamental relationships between angles!
This tutorial covers the essential angle pair rel...
2
Key Concepts & Vocabulary
TermDefinitionExample
Complementary AnglesTwo angles whose measures have a sum of 90 degrees.If ∠A measures 35° and ∠B measures 55°, they are complementary because 35° + 55° = 90°.
Supplementary AnglesTwo angles whose measures have a sum of 180 degrees.If ∠C measures 110° and ∠D measures 70°, they are supplementary because 110° + 70° = 180°.
Adjacent AnglesTwo angles that share a common vertex and a common side, but have no common interior points.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.
Linear PairA pair of adjacent angles whose non-common sides are opposite rays, forming a straight line. Angles in a linear pair are always supplementary.Two angles that form a straight line along the floor. If one angle is 130°,...
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. Set the sum of their measures equal to 90 to solve for an unknown.
Supplementary Angles Sum (Linear Pair Postulate)
If ∠A and ∠B form a linear pair, then m∠A + m∠B = 180°
Use this rule when two adjacent angles form a straight line. Set the sum of their measures equal to 180 to find a missing angle.
Vertical Angles Congruence Theorem
If ∠A and ∠B are vertical angles, then m∠A = m∠B
Use this theorem when you have two intersecting lines. Set the measures of the opposite angles equal to each other to solve for a variable.
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
In proving two triangles congruent using Angle-Side-Angle (ASA), a student knows that a side and one adjacent angle are congruent. To complete the proof, they need the other adjacent angle. They are given that an exterior angle at that vertex is 110°. What is the measure of the needed interior angle?
A.20°
B.70°
C.110°
D.250°
Challenging
Two intersecting lines form angles 1, 2, 3, and 4. A student incorrectly sets up the equation m∠1 + m∠2 = m∠3 + m∠4. This equation is only true if...
A.The lines are parallel.
B.The lines are perpendicular.
C.m∠1 = m∠2.
D.This equation is always true.
Challenging
Ray OB bisects right angle ∠AOC. Ray OD and Ray OE are opposite rays. What is the measure of ∠DOE?
A.45°
B.90°
C.135°
D.180°
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 "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 complementary, supplementary, vertical, and adjacent angles when presented in diagrams with at least 80% accuracy; Solve for unknown angle measures in complementary and supplementary angle problems, showing all work….
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.