SOLUTION: I wrote the book and the page of the problem. Also the problem itsself.
International Mathematics for the Middle Years 3
p274
N3 c) Sharon makes a regular pentagon from the
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Question 1117558: I wrote the book and the page of the problem. Also the problem itsself.
International Mathematics for the Middle Years 3
p274
N3 c) Sharon makes a regular pentagon from the three isoscales triangles as shown. Find the sizes of the angles in triangle.
(You cannot see the diagram. One isoscales triangle is from left facing out straight, other is on the right and is conqruent to the one from the left. In the middle there is one more. Left isoscales triangle — b degrees, a degrees, b degrees. Right isoscales triangle — b degrees, a degrees, b degrees. Middle isoscales triangle — d degrees, c degrees, d degrees.)
I know it is hard to understand but thank you who will solve it!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The sum of the interior angles of a pentagon is (180)\ = 540)
degrees. Since it is a regular pentagon, the interior angles are all congruent, hence each interior angle measures 108 degrees. Then 108 degrees is the measure of the apex angle of the two identical isosceles triangles.
Therefore 
. But the sum of the angles in any triangle is 180 degrees, so 
. From that we get 
after substituting for 
.
One vertex of the pentagon contains three angles, one from each of the three isosceles triangles, namely angles 
, 
, and . We know that these three angles must add up to 108, and we know that two of them measure 36, so the third one, must be 36 degrees as well.
Then, 
. You can calculate the size of 
yourself. Oh, and by the way, it is isosceles, not isoscales. Yes, spelling counts.
John
My calculator said it, I believe it, that settles it
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