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September 07, 2010 Bell Ringers – Sept 7 1. The sum of two numbers is 90 and one number is 4 times the other. Write the equation and solve to find the numbers. 2. In the diagram, MN bisects ∠PMQ and m∠PMQ = 122º. Find m∠PMN. Illustrate with a picture. Classify ∠PMN. 3. M is the midpoint of the segment. Find EM. • 8x - 6 7x E G M 4. Find the coordinates of the midpoint of the segment with the given endpoints. P(-8, -7) and Q(11, 5) September 07, 2010 1.5 Angle Relationships Complementary angles - two angles whose sum is 90º • Each angle is the Supplementary angles - 2 angles whose sum is 180º • Each angle is the Complementary and supplementary angles can be Adjacent angles - 2 angles that share a common vertex and common side. 3 1 4 2 7 5 6 8 September 07, 2010 Ex 1: What is the complement and supplement of each angle? a) 34º b) 96º Ex 2: Use the diagram to the right to answer the following questions. a) Name a pair of supplementary angles 2 3 b) Name a pair of complementary angles 1 5 4 c) Name a pair of adjacent angles Ex 3: Find x and y. •N (5x+30)º (4x+15)º P (3y-15)º O (3y+15)º • L • M • Guided Practice 1. Given that ∠1 is a complement of ∠2 and m∠1=8º, find m∠2. 2. ∠LMN and ∠PQR are complementary angles. Find the measures of the angles if m∠LMN = (4x - 2)º and m∠PQR = (9x + 1)º. 3. Two roads intersect to form supplementary angles, ∠XYW and ∠WYZ. Find m∠XYW and m∠WYZ. •W • X (2x + 14)º (4x - 20)º Y • Z September 07, 2010 vertical angles: 2 ∠s whose sides form 2 pairs of opposite rays. linear pair: 2 adjacent ∠s whose noncommon sides form opposite rays. 1 2 3 6 5 4 Ex 4: Use the diagram to answer the following a) Are ∠1 and ∠2 a linear pair? b) Are ∠4 and ∠5 a linear pair? 2 1 3 5 4 a) Are ∠5 and ∠3 vertical angles? Ex 5: T and V are supplementary. The measure of T is half of the measure of V. Find the measure of each angle. Guided Practice 5. Two angles form a linear pair. The measure of one angle is 5 times the measure of the other. Find the measure of each angle. Homework Pages 38-41 #1, 2, 4-7, 9-15 odd, 16, 17-27 odd, 30-54 even, 57