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O A. Yes, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 150° = 360°. O B. No, because a vertex figure cannot be formed with different types of polygons. O C. No, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 155° = 365°, so there is a slight overlapping of the polygons. O D. No, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 145° = 355°, so there is a slight gap in the vertex.

O A. Yes, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 150° = 360°. O B. No, because a vertex figure cannot be formed with different types of polygons. O C. No, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 155° = 365°, so there is a slight overlapping of the polygons. O D. No, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 145° = 355°, so there is a slight gap in the vertex.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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O A. Yes, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 150° = 360°. O B. No, because a vertex figure cannot be formed with different types of polygons. OC. No, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 155° = 365°, so there is a slight overlapping of the polygons. O D. No, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 145° = 355°, so there is a slight gap in the vertex.
Transcribed Image Text:O A. Yes, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 150° = 360°. O B. No, because a vertex figure cannot be formed with different types of polygons. OC. No, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 155° = 365°, so there is a slight overlapping of the polygons. O D. No, because the sum of the measures of the interior angles of the four polygons is 60° + 60° + 90° + 145° = 355°, so there is a slight gap in the vertex.
Wailea noticed that, since two adjacent equilateral triangles, a square, and a dodecagon form a vertex figure such as that shown at A, there should be a semiregular tiling in which this vertex figure occurs at every vertex. (a) Is Wailea correct that these four polygons create a vertex figure at A? (b) Explain to Wailea why the vertex figure does not extend to a semiregular tiling. B
Transcribed Image Text:Wailea noticed that, since two adjacent equilateral triangles, a square, and a dodecagon form a vertex figure such as that shown at A, there should be a semiregular tiling in which this vertex figure occurs at every vertex. (a) Is Wailea correct that these four polygons create a vertex figure at A? (b) Explain to Wailea why the vertex figure does not extend to a semiregular tiling. B
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