Find measures of complementary, supplementary, vertical, and adjacent angles

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...

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°,...

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.