Geometry
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| This regular pentagon has a square inside with it's vertices touching the midpoints of the pentagon. Find the value of the missing angle. |
A box of biscuits
A box of biscuits contains 36 biscuits. 20 biscuits have foil wrappers. 15 are chocolate biscuits with foil wrappers. If 9 are not chocolate and do not have a foil wrapper, then how many chocolate biscuits are there?
We know that the square is touching the midpoints of the pentagon so the triangle that uses a side of the square would be isosceles. Also, We know that each angle of a pentagon is 108° so the other angles of that isosceles triangle would be 36°.
ReplyDeleteIf you go to the angle of the triangle closest to the red angle we are trying to find, then you will see that if you add the 36° of the triangle to the 90° of the square, you will get 126°. Also, after you have the red angle, 126° + the red angle would give you 180° because it is on a straight line. So now, all you need to do is 180° - 126° which is 54° so 54° is your answer.