Results 1 to 5 of 5

Math Help - Find the measures of angles of pentagram?

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    19

    Find the measures of angles of pentagram?

    What is the sum of the measures of angles A, B, C, D, and E?



    I really need at least some kind of hint here, because I have no idea where to begin. No information is given for the picture.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,639
    Thanks
    1592
    Awards
    1
    I have added five letters to your diagram.
    The sum of the angles in the pentagon, KJLMN, is 3\pi =540^\circ . WHY?
    In \Delta\text{ANK} the sum \angle A + \angle 1 + \angle 2 = 180^ \circ.
    Moreover, by the external angle theorem \angle K = \angle A + \angle 1.
    If you do this for each of the other four “external triangles” and all five you will see the answer.
    Attached Thumbnails Attached Thumbnails Find the measures of angles of pentagram?-pentagram.gif  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2008
    Posts
    19
    I did that before, and it got me no where. All I get is that:

    <br /> <br />
\angle N = \angle E + \angle 4<br />
    <br /> <br />
\angle M = \angle D + \angle 6<br />

    etc.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,639
    Thanks
    1592
    Awards
    1
    Quote Originally Posted by Rinnie View Post
    I did that before, and it got me no where.
    You did not take it far enough then.
    \angle K + \angle N = 2\angle A + \angle 1 + \angle 2 = \angle A + 180^ \circ .
    Do that all around the "inside" pentagon.
    Remember that sum of the angles in, KJLMN, is 540^\circ
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Rinnie View Post
    What is the sum of the measures of angles A, B, C, D, and E?



    I really need at least some kind of hint here, because I have no idea where to begin. No information is given for the picture.
    When you move a single vertex (at least if it remains on the same side of the line segment joining the oposite vertices) the angle sum remains invariant.

    Since the given figure can be transformed by a sequence of such moves into a regular pentagram, the angle sum of the regular pentagram is equal to the angle sum of the given figure.

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. measures of the angles
    Posted in the Geometry Forum
    Replies: 4
    Last Post: December 4th 2010, 05:05 PM
  2. Find measures of angles, massive error !
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: December 14th 2009, 02:48 AM
  3. Help with measures of angles
    Posted in the Geometry Forum
    Replies: 4
    Last Post: November 7th 2008, 08:38 AM
  4. Angles and Radian Measures
    Posted in the Geometry Forum
    Replies: 4
    Last Post: September 3rd 2008, 07:03 PM
  5. Angles and Radian Measures
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: August 22nd 2008, 01:08 PM

Search Tags


/mathhelpforum @mathhelpforum