A regular pentagon with centre $C$ is shown. The value of $x$ is
(A) 144
(B) 150
(C) 120
(D) 108
(E) 72

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-149.jpg?height=336&width=347&top_left_y=618&top_left_x=1366)
A regular pentagon with centre $C$ is shown. The value of $x$ is
(A) 144
(B) 150
(C) 120
(D) 108
(E) 72

![](https://cdn.mathpix.com/cropped/2024_04_20_688a3b42f69739f2e244g-280.jpg?height=377&width=382&top_left_y=657&top_left_x=1359)

## Solution

Join $C$ to each of the remaining vertices, as shown. Since the pentagon is regular, each of the small angles at $C$ has measure $360^{\circ} \div 5=72^{\circ}$.

Thus, the value of $x$ is $2(72)=144$.

![](https://cdn.mathpix.com/cropped/2024_04_20_688a3b42f69739f2e244g-280.jpg?height=372&width=382&top_left_y=1142&top_left_x=1300)

ANSWER: (A)