Rays ab and bc are perpendicular. point d lies in the interior of abc. if abd = 3r + 5 and the measure of dbc = 5r - 27, find the measure of abd and dbc

abd = 47, dbc = 43 The fact that the rays ab and bc are perpendicular tells you that the angle abc is 90 degrees. Given that the point d is within the interior of the angle abc tells you several things. Namely that the angle abd is less than or equal to 90, the angle dbc is also less than or equal to 90, and finally that the sum of the angles abd and dbc total to exactly 90. So write the formula abd + dbc = 90 Substitute the formulas given for the angles (3r + 5) + (5r - 27) = 90 Get rid of the parenthesis 3r + 5 + 5r - 27 = 90 Merge the terms 8r - 22 = 90 Add 22 to both sides 8r = 112 Divide both sides by 8 r = 14 Now given r = 14, calculate both abd and dbc abd = 3r + 5 = 3*14 + 5 = 42 + 5 = 47 dbc = 5r - 27 = 5*14 - 27 = 70 - 27 = 43

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