Answer to Question #197469 in Geometry for Andu

Question

The sum of the angles in each quadrilateral is 360 °. For example, in a rectangle 4 x 90 ° = 360 ° Gent writes: 5 x 90⁰ = 450⁰, so the sum of the angles in each pentagon must be 450 °.

Is he right? If not, give the correct answer.

Answer 1

Unlike a rectangle, a Pentagon cannot have 5 right angles except they are all obtuse. A Pentagon can only have at most 3 right angles. Therefore, Gent's approach is wrong. To see this mathematically:

$\text{ Sum of interior angles= } (n-2) \times 180°$

Since Pentagon has 5 sides, n=5. Thus:

$=(5-2) \times 180°\\ =3 \times 180°\\ =540°$

Therefore, Gent is wrong.