Identify complementary, supplementary, vertical, adjacent, and congruent angles

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...

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...

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.