Help with geometry homework?

The questions correspond to diagrams, so here's the link to a pic of them:

http://i284.photobucket.com/albums/ll30/izetehuber...

And it would help if you could explain how you did it.

Thanks. :D

Update:

I mean all of the questions....-3-

4 Answers

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  • 1 decade ago
    Favorite Answer

    Deidara! What an innovative way to do your homework! I hope your teacher is OK with this, and I hope you are not taking the easy way out. Try to develop your understanding of the principles of geometry, and you will get there.

    Q6. First you need to know that the sides of a regular hexagon are all equal to one another. i.e. AB=BC=CD=DE=EF=FA.

    Next, all four sides of the square ABGH are equal.

    So AB=BG. ----------(1)

    Now AB=BC (sides of regular hexagon),--------(2)

    => BG=BC => GBC is an isoceles triangle.

    Next we determine angle GBC.

    We know angle ABC =120 deg (internal angle of regular hexagon)

    => angle GBC= ABC-ABH =120-90= 30 deg.

    Which means angle BGC = (180-30)/2 = 75 deg

    => x = angle DGC = 180-75 = 105 deg (straight line BGD)

    Q7. A regular pentagon has five equal sides

    => EA = ED and EAD is an isoceles triangle.

    Internal angle of regular pentagon = 108 deg

    => angle EAD =108 deg.

    So angle EAD = (180 -108)/2 = 36 deg

    angle DAB = EAB- EAD = 108 - 36 = 72 deg

    => x = GAB - DAB = 90 - 72 = 18 deg.

    Q8. Angle HFD is the sum of HFB and BFD. So we will find HFB an BFD and add them together.

    (a)Calculate angle HFB

    In isoceles triangle GHF, angle HGF = GAB + AGF = 60 +90 = 150 deg

    => angle HFG = (180-150)/2 = 15 deg

    So angle HFB = GFB - HFG = 90 - 15 = 75 deg

    (b) Calculate angle BFD

    EFD is an isoceles triangle,and angle FED = 108 deg

    => angle EFD = (180 -108)/2 = 36 deg

    => angle BFD = BFE - EFD = 108 - 36 = 72 deg

    So, angle HFD = 75 + 72 = 147 deg.

    To tackle these problems you needed to understand/know :

    1) How to calculate internal angles of regular polygons (triangle, square, pentagon, hexagon) i.e. 3, 4, 5 and six sided figures. I have assumed you know this and have not shown the working.

    2) As you can see, extensive use is made of isoceles triangles in order to calculate angles. You will come across this time and again in geometry.

    Hope I have helped, not only with your homework, but also in enhancing your appreciation of geometry. These problems were quite challenging.

  • 1 decade ago

    On #6, angle ABC = 120 and angle ABG = 90 so angle GBC = 30. Triangle GBC is isosceles, so its other two angles

    are (180 - 30) / 2 or 75. And x is a linear pair with one of those so x = 180 - 75 = 105

    s

  • 1 decade ago

    #6 above is correct

    #7

    each interior angle on a pentagon is 108 degrees

    triangle AED is isosceles

    since angle E is 108, angle EAD and angle EDA are 180-108/2

    or 36 degrees

    angle EAB is also 108

    subtract 36 of angle EAD, to find angle DAB

    angle DAB is 72 degrees

    angle GAB(90) is made up of angle DAB(72) and angle x

    x= 90-72

    x=18

    #8

    I have no idea.

  • Anonymous
    7 years ago

    You can see the source link.

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