# Why the tetrahedron is equal to the angle of 109.5degrees but it says in an article that if you divide the number of bonds thats the angle but when i divide 4 to 360 the answer is 90 they did not match pls answer my question tnx?

Sep 10, 2017

A tetrahedron is not flat...

#### Explanation:

If you have a flat symmetrical molecule such as Borane $B {H}_{3}$ then dividing ${360}^{\circ}$ by the number of bonds makes sense, but in the case of a three dimensional tetrahedral molecule such as Methane $C {H}_{4}$ it does not.

You could model the shape by imagining a carbon atom at $\left(0 , 0 , 0\right)$ and hydrogen atoms at: $\left(1 , 1 , 1\right)$, $\left(1 , - 1 , - 1\right)$, $\left(- 1 , 1 , - 1\right)$ and $\left(- 1 , - 1 , 1\right)$ (alternate vertices of a cube form the vertices of a tetrahedron).

Then the angle between the line joining $\left(0 , 0 , 0\right)$ and $\left(1 , 1 , 1\right)$ and the line joining $\left(0 , 0 , 0\right)$ and $\left(1 , - 1 , - 1\right)$ is:

$\arccos \left(\frac{< 1 , 1 , 1 > . < 1 , - 1 , - 1 >}{\left\mid < 1 , 1 , 1 > \right\mid \cdot \left\mid < 1 , - 1 , - 1 > \right\mid}\right) = \arccos \left(- \frac{1}{3}\right) \approx {109.5}^{\circ}$