Guest Posted October 28, 2011 Report Share Posted October 28, 2011 B. The attached diagram shows a regular pentagon and a regular hexagon that overlap. What is the value of x? Quote Link to comment Share on other sites More sharing options...
0 Thalia Posted October 28, 2011 Report Share Posted October 28, 2011 By regular, do you mean all the sides and angles are equal? 108 degrees? Quote Link to comment Share on other sites More sharing options...
0 robo Posted October 28, 2011 Report Share Posted October 28, 2011 The diagram is not correct for a regular hexagon and regular pentagon. If they share a coordinate, they can not share the opposite side. Anyhow, from the diagram it seems you are asking for the internal angle of a regular pentagon which Thalia has answered. But then why is the hexagon in the picture? Something is missing. Please clarify. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 28, 2011 Report Share Posted October 28, 2011 I think the diagram is right. Is the answer 84 degrees? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 28, 2011 Report Share Posted October 28, 2011 The problem: with common vertex, determine angle between side of pentagon and side of hexagon: To solve: we know that interior angles of a polygon of n sides total (n-2)*180. Using this, we can determine each interior angle of a hexagon = 120 degrees and each interior angle of a pentagon = 108 degrees. All we need to do is calculate the angle of pentagon with horizontal side of hexagon and subtract from 120 degrees. A vertical through the vertex bisects the interior angle of the pentagon, forming a 108/2 =54 degree angle from the vertical. 90-54 degrees=36 degrees from horizontal. 120-36 degrees = 84 degrees Answer = 84 Degrees Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 28, 2011 Report Share Posted October 28, 2011 The diagram is not correct for a regular hexagon and regular pentagon. If they share a coordinate, they can not share the opposite side. Anyhow, from the diagram it seems you are asking for the internal angle of a regular pentagon which Thalia has answered. But then why is the hexagon in the picture? Something is missing. Please clarify. You are looking at the wrong pentagon. If you label the 4 intersections across the bottom as A,B,C and D. A-C is the base of the regular pentagon and B-D is the base of the regular hexagon. The pentagon whose base is B-C is an irregular pentagon. Quote Link to comment Share on other sites More sharing options...
0 robo Posted October 28, 2011 Report Share Posted October 28, 2011 You are looking at the wrong pentagon. If you label the 4 intersections across the bottom as A,B,C and D. A-C is the base of the regular pentagon and B-D is the base of the regular hexagon. The pentagon whose base is B-C is an irregular pentagon. Thanks thoughtfulfellow. Now the question does make sense. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 31, 2011 Report Share Posted October 31, 2011 (edited) thoughtfulfellow's answer is correct (I believe), though I went about it a different way. Start with the facts: a regular hexagon has six angles of 120 degrees, and a regular pentagon has five angles of 108 degrees. Notice then that there is a new, non-regular pentagon being formed by the angle marked x, along with two angles from the regular hexagon and two from the regular pentagon. So take the total degrees in the new pentagon (540), subtract the two angles from the regular hexagon and the two from the regular pentagon, and you have 84. Mathematically: 540-120(*2)-108(*2) = 84. Edited October 31, 2011 by statsman Quote Link to comment Share on other sites More sharing options...
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B. The attached diagram shows a regular pentagon and a regular hexagon that overlap.
What is the value of x?
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