2009 CEMC Pascal Problems/Problem 5

Problem

In the diagram, the value of $x$ is

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$\text{ (A) }\ 15 \qquad\text{ (B) }\ 20 \qquad\text{ (C) }\ 24 \qquad\text{ (D) }\ 30 \qquad\text{ (E) }\ 36$

We can use the fact that the sum of the angles must be $360^{\circ}$ due to the angles being around a full circle. Setting up an equation, we have:

$x + 2x + 5x + 4x = 360^{\circ}$

Adding like-terms, we get:

$12x = 360^{\circ}$

Dividing both sides by $12$ , we get:

$x = \frac{360^{\circ}}{12} = \boxed {\textbf {(D) } 30}^{\circ}$

~anabel.disher