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Supplementary and Complementary Angle Pairs

Find missing angle measures for supplementary or complementary angles.

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Leaning Towers

Credit: Zhi Yong Lee
Source: http://www.flickr.com/photos/zh1yong/349923193/
License: CC BY-NC 3.0

Have you ever heard of the Leaning Tower of Pisa? This famous building was supposed to be built standing straight up and down, but it gradually tilted with passing time, even as it was being constructed. The angle on the right side of the tower and the angle on the left are supplementary angles. Together, they add up to 180 degrees, or a straight angle.

How the Tower Tilted and How It Straightened Up

Builders began work on the Leaning Tower of Pisa in 1173. A donor gave money to build a fabulous bell tower for the cathedral of the Italian city of Pisa. The tower tilted right from the beginning. The foundation was weak and the ground was soft, so it couldn't support the weight of the structure. Throughout the construction process, the builders tried to change the plans to correct for the tilt. They built the third, fifth, and eighth floors crooked in the hopes that it would make the tower stand straight! After 200 years, they finally finished the tower and gave up. The Leaning Tower was doomed to lean.

Credit: Rauschenfels von Steinberg
Source: http://commons.wikimedia.org/wiki/File:Pisa_basilica_tower_c1830.jpg
License: CC BY-NC 3.0

Over time, the tower leaned further and further to the side. It was feared that the tower would collapse. Beginning in the 1960s, the Italian government convened a team of engineers, mathematicians, and historians to brainstorm ways to stabilize the tower. They wanted to stop the decline but leave it at an angle. After all, the tower is a major tourist attraction precisely because it leans. In 1990, after more than two decades of deliberation, a group of architectural experts began work on the tower to straighten it out. They added lead counterweights to balance the tower and removed soil from underneath the raised side. In 2001, the tower was reopened to the public. The tower still leans, but it's once again stable and safe for visitors—at least for the next 200 years.

See for yourself: http://www.huffingtonpost.com/2011/08/22/watch-leaning-tower-of-pi_n_933027.html

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The Leaning Tower of Pisa currently tilts at a 3.99° angle. What is the smaller angle between the tower and the ground? What is the larger angle between the tower and the ground?

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Image Attributions

  1. [1]^ Credit: Zhi Yong Lee; Source: http://www.flickr.com/photos/zh1yong/349923193/; License: CC BY-NC 3.0
  2. [2]^ Credit: Rauschenfels von Steinberg; Source: http://commons.wikimedia.org/wiki/File:Pisa_basilica_tower_c1830.jpg; License: CC BY-NC 3.0

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