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hendricks_beginning_algebra_1e_ch1_3

When two lines intersect one another, four angles are created. Angles opposite from one another are vertical or opposite angles. These angles have equal measure. a b c d In this figure, angles a and c are vertical angles and angles b and d are vertical angles. a = c and b = d ������������ Angles a and b form a straight angle. So, a + b = 180°. Angles b and c form a straight angle. So, b + c = 180°. Angles c and d form a straight angle. So, c + d = 180°. Angles d and a form a straight angle. So, d + a = 180°. �� ������������������������ ������������������ Find the measure of each unknown angle. 5a. 5a a 5b. 9x – 6 7x + 2 Solutions 5a. The two angles form a straight angle and, therefore, have a sum of 180°. 5a + a = 180 6a = 180 6a 6 = 180 6 a = 30 Express the relationship. Combine like terms. Divide each side by 6. Simplify. Since a is 30°, the other angle is 5(30) or 150°. 5b. The two angles are vertical angles and, therefore, have equal measure. 9x - 6 = 7x + 2 9x - 6 - 7x = 7x + 2 - 7x 2x - 6 = 2 2x - 6 + 6 = 2 + 6 2x = 8 2x 2 = 8 2 x = 4 Express the relationship. Subtract 7x from each side. Simplify. Add 6 to each side. Simplify. Divide each side by 2. Simplify. Since x = 4, the measures of the angles are 9(4) - 6 = 36 - 6 = 30° and 7(4) + 2 = 28 + 2 = 30°. Student Check 5 Find the measure of each unknown angle. a. a 2a + 12 b. 2a + 10 3a – 40 144 Chapter 2 Linear Equations and Inequalities in One Variable


hendricks_beginning_algebra_1e_ch1_3
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