Questions: In the figure below, h is perpendicular to I and j is perpendicular to k. Find the values of y and z.

Solution Steps

Since lines _h_ and _l_ are parallel, and line _j_ is a transversal, the angle _y_ and the angle measuring 71° are corresponding angles. Corresponding angles are congruent, therefore: \(y = 71^{\circ}\)

Since lines _j_ and _k_ are parallel and line _h_ is a transversal, the angle measuring (5z - 109)° and the angle adjacent to the 71° angle are corresponding angles. These two angles are congruent. The angle adjacent to the 71° angle and the 71° angle itself are supplementary angles, meaning they sum up to 180°. Let's call this adjacent angle _x_. Therefore: \(x + 71 = 180\) \(x = 180 - 71\) \(x = 109^{\circ}\)

Since angle _x_ and the angle measuring (5z - 109)° are corresponding angles and therefore congruent: \(5z - 109 = 109\) \(5z = 109 + 109\) \(5z = 218\) \(z = \frac{218}{5}\) \(z = 43.6\)

Final Answer