Find the value of X AND Y: Show your work.

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Question:

Find the value of X AND Y: Show your work.

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We are given:                                                                                                         AB = 7x + 10 BD = 9x - 2∠DBC = 9y - 9∠ABC = 90°AB = BDSolving for x:                                                                                                           We are given that AB = BD7x + 10 = 9x - 2               [since AB = 7x+10 and BD = 9x-2]10 = 2x - 2                       [subtracting 7x from both sides]2x = 12                            [adding 2 on both sides]x = 6                               [dividing both sides by 2]Hence, x = 6Solving for y:_______________________________________________   We know that AD is a straight line,So, ∠ABC and ∠DBC must form a linear pair∠ABC + ∠DBC = 180°90 + 9y-9 = 1809y - 9 = 90             [subtracting 90 from both sides]9y = 99                  [adding 9 on both sides]y = 11                      [dividing both sides by 9]Hence, y = 11

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