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Angle Classification Acute angles measure more than 0 degrees but less than 90 degrees. Right angles measure exactly 90 degrees. Perpendicular lines form right angles. Obtuse angles measure greater than 90 degrees but less than 180 degrees. A straight angle (line) has a measure of 180 degrees. Angle Addition Postulate If D is in the interior of ABC , then mABD mDBC mABC . Angle Relationships Adjacent angles – Coplanar angles that have a common vertex and one common side, but no common interior points BAC and CAD B A D Vertical angles – Two non-adjacent angles formed by two intersecting lines 1 & 2, 3 & 4 1 Linear pair – Two adjacent angles whose non-common sides are two rays going in opposite direction 1 & 2 Complementary angles – Sum of the measures of the two angles is 90 degrees. Supplementary angles – Sum of the measures of the two angles is 180 degrees. If two angles form a linear pair, they are supplementary. C 1 3 4 2 2 30o 60o 120o 60o Angle Theorems Vertical angles are congruent. If two angles are supplementary to the same angle or to congruent angles, they are congruent. If two angles are complementary to the same angle or to congruent angles, they are congruent. Examples Use the figure to answer problems #1 - 2 below. C A O B D 1. If m AOC = 16x – 20 and m BOD = 13x+7, find the value of x and the degree measure of the two angles. x = 9, m AOC = m BOD = 124 º 2. If m AOB = 4x + 15 and m AOC = 3x + 25, find the degree measures of AOB and AOC . x = 20, m AOB = 95 º and m AOC = 85 º Solve the following problems using the given information. 3. X and Y are complementary angles. If m X = 3x + 7 and m Y = 6x+20, find the value of x and the degree measure of each angle. x = 7, m X = 28 º, m Y = 62 º 4. The measure of the complement of an angle is one-fourth the measure of the supplement of the angle. Find the measure of the angle. The angle measures 60 º. x = angle 90 – x = complement 180 – x = supplement complement = (1/4)supplement 90 – x = (1/4)(180 – x) 360 – 4x = 180 – x 180 = 3x x = 60