Lesson 2: Transversals - Combining Properties Example 2

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A video demonstrating the solution to a combination of transversal properties problem is provided.



EXAMPLE 2

The large yellow piece of the mosaic stainglass window is broken and needs to be replaced. Precise angle measures are required for each of the six angles on the piece of glass in order to cut a replacement.



The window was designed using multiple sets of parallel and perpendicular lines, as indicated on the diagram above. One set of the diagonal parallel lines forms a 50° angle with the vertical, and the other set of diagonal parallel lines forms a 75° angle with the vertical, as shown on the diagram below.



What are the six angle measures needed to ensure a proper replacement of the broken piece of glass?

Solution


Angle Isolated diagram Transversal rules used Angle
1 ∠1 can be calculated by knowing that it is the interior supplementary angle of 50°.

180° − 50° = 130° 		∠1 is 130°
2 From the context of the question, these lines are perpendicular. ∠2 is 90°
3 The interior angle measures of a triangle add to 180°. At the lower vertex of the upper left triangle, the angle measure corresponds to the given 50° angle.

At the top left vertex of that same triangle, the angle measure is 90°(a right angle).

At the top right vertex of that same triangle, the angle measure is:

180°− 50°− 90° = 40°

∠3 is supplementary with the 40° angle.

180° − 40° = 140° 		∠3 is 140°
4 ∠4 can be calculated by knowing that it is the interior supplementary angle of 50°.

180° − 50° = 130° 		∠4 is 130°
5 ∠5 can be calculated by knowing that it is the interior supplementary angle of 75°.

180° − 75° = 105° 		∠5 is 105°
6 The interior angle measures of a triangle add to 180°. One angle measure in the lower left triangle is given as 50°.

A second angle is the alternate interior angle of 75°.

The third angle measure is:

180° − 50° − 75° = 55°

∠6 is supplementary with the 55° angle.

180° − 55° = 125° 		∠6 is 125°


There are multiple strategies to calculate missing angles. This is one solution to the problem.


Now, it is your turn! Complete the questions in your Chapter 6, Lesson 2 Practice Makes Perfect that refer to Combining Properties.



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