ABCDE is a regular pentagon. A line is drawn from B to E. What is the size of angle ABE?
The internal angles of a regular pentagon are 108°.
(If you need proof I like to use external angles, rather than memorizing an internal angle formula: 360°/5 = 72°
=> internal angle = 180°-72° = 108°)
Drawing a line from B to E will form an obtuse Isosceles triangle with A forming the obtuse angle. Angle A is not affected, and remains 108°.
The sum of all the angles of a triangle are equal to 180°, and our triangle is isosceles, so half the remaining amount (after subtracting angle A) is equal to the two acute angles (ABE and BEA).
1/2(180°-108° = 72°)
A regular pentagon is convex. By taking a regular pentagon and shortening or lengthening one or more sides, an infinite number of possible convex pentagons can be created. A convex polygon is defined as a polygon such that all internal angles are less than or equal to 180 degrees, and a line segment drawn between any two vertices remains inside the polygon. It is possible to have non-convex (concave) pentagons; there are infinite number possible…
today i took my grade 9 EQAO math test and this was a question on it, the hardest on the test it gave me a picture of a five point star (drawn as you would without lifting the pecnil, with five lines). I had to solve for angles abcde (the angles within the point of the star) withough a protractor, and no measurements given. impossible you may say, but there is a sure way that…