 • Slides: 9 Measure and Explore Angles Adjacent Angles Adjacent angles are two angles that lie in the same plane, have a common vertex, and a common side, but no common interior point. 1 2 3 4 Vertical Angles Vertical angles are two nonadjacent angles formed by two intersecting lines 4 3 Vertical angles are ALWAYS congruent 1 2 Angles 1 and 3 are vertical; Angles 2 and 4 are vertical. Linear Pair A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays. Linear pairs have a sum of 180 degrees. 1 2 Angles 1 and 2 form a linear pair Complementary Angles Complementary angles are 2 angles whose measures have a sum of 90 degrees Complementary angles can be adjacent or nonadjacent 200 700 Supplementary Angles 520 1280 Supplementary angles are 2 angles whose measures have a sum of 180 degrees. Supplementary angles can be adjacent or nonadjacent. Perpendicular Lines Perpendicular lines intersect to form 4 right angles Perpendicular lines intersect to form congruent adjacent angles Segments and rays can be perpendicular to lines or other segments and rays The right angle symbol in the figure indicates the lines are perpendicular Examples Lines p and q intersect to form adjacent angles 1 and 2. If m<1 = -3 x+18 and m<2 = 8 y-70, find the values of x and y so that p is perpendicular to q. X = -24, y = 20 Examples, continued… If m<A = 75, what are the complement and supplement of <A? C = 15, S = 105 m<B = x. Name the complement and supplement of <B. C = 90 -x, S = 180 -x The supplement of an angle is twice the measure of the angle. Find the angle and its supplement. 60, 120