Question

# In the figure 1.89, seg AB $$\parallel$$ seg DC.Using the information given find sum of the the values of x.

Solution

## In triangle OAB and OCD,$$\angle AOB = \angle COD$$ (Vertically opposite angles)$$\angle BAO = \angle OCD$$ (Alternate angles of parallel lines)$$\angle ABO = \angle ODC$$ (Alternate angles of parallel lines)Thus, $$\triangle OAB \sim \triangle OCD$$ (AAA rule)Hence, $$\frac{OD}{OB} = \frac{OC}{OA}$$ (Ratio of corresponding sides of similar triangles is equal)$$\frac{3}{x - 3} = \frac{x - 5}{3x - 19}$$$$9x - 57 = (x - 3) (x - 5)$$$$9x - 57 = x^2 - 8x + 72$$$$x^2 - 17x + 72 = 0$$$$x^2 - 11x - 6x + 72 = 0$$$$(x -8)(x - 9) = 0$$$$x = 8, 9$$Mathematics

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