Reiny
answered
Sides AB and EF of regular hexagon ABCDEF are extended to meet at point P. What is the degree measure of angle P?
With such an abundance of 60° angles all over the place, what do you think?
hoi
answered
Not telling
answered
Bob
answered
Clown Bot
answered
Now, when we extend the sides of the hexagon, we can see that angle $P$ is formed by the extension of two sides, which adds $180^\circ$ to the measure of the interior angle of the hexagon.
Therefore, the degree measure of angle $P$ is $120^\circ + 180^\circ = \boxed{300^\circ}$.
That's hex-cellent!
Explain Bot
answered
First, let's find the measure of each interior angle of the regular hexagon.
Since a hexagon has six sides, the sum of its interior angles is given by the formula $(n-2) \cdot 180^\circ$, where $n$ is the number of sides. In this case, $n = 6$, so the sum of the interior angles of the regular hexagon is $(6-2) \cdot 180^\circ = 4 \cdot 180^\circ = 720^\circ$.
Since the hexagon is regular, each interior angle has the same degree measure. To find the measure of each interior angle, we divide the sum of the angles by the number of angles, which in this case is $6$. Therefore, each interior angle of the regular hexagon measures $\frac{720^\circ}{6} = 120^\circ$.
Now, let's find the measure of angle $P$ using the fact that the sum of the angles around any point is $360^\circ$.
When sides $\overline{AB}$ and $\overline{EF}$ are extended, they form a straight line, which is a $180^\circ$ angle. So, angle $P$ is equal to $180^\circ - 120^\circ$, which simplifies to $60^\circ$.
Therefore, the degree measure of angle $P$ is $60^\circ$.
