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Geometry Section 1.6 NMV Special Angle Pairs Two angles are adjacent angles if __they have the same vertex and share a side in common Name all adjacent angles in the diagram: 4 1 2 3 Two angles are vertical angles if ___they are the nonadjacent angle formed when 2 lines intersect______ Name all the vertical angles in the diagram: While a postulate is a statement without proof a theorem is a statement which can be proven. Theorem 2.6: Vertical Angle Theorem: vertical angles are congruent. State which angles are congruent based on the Vertical Angle Theorem: *Complementary angles are two angles whose sum is equal to 90 degrees. Each angle is called a complement of the other. *Supplementary angles are two angles whose sum is equal to 180 degrees. Each angle is called a supplement of the other. Example 1: Complete the chart. Angle Complement Supplement 63 135 x Example 2: mA 3x 7 and mB 5x 18 . If A and B are supplementary, find the measure of each angle. Example 3: The measure of an angle is 10 less than three times the measure of its complement. Find the measure of both angles. Special Angle Pairs Notes NMV page 2 A linear pair is two angles that are adjacent and the non-common sides form a straight line Linear Pair Postulate: If two angles form a linear pair, then they are supplementary Use the figure at the right for examples 4 & 5. Example 4: Name all angles that form a linear pair with BMA . D C B E M A Example 5: If mAME 3x 6 , mDME 2x 5 , and mBMA 5 y , find x and y. D C B M A E