Question

problem 17: find x and y. after you enter your answer press go. x = y =

Explanation:

Step1: Recall angle - sum property

The sum of angles around a point is $360^{\circ}$. So $x + 3x+2x + y=360$.

Step2: Combine like - terms

Combining the $x$ terms, we get $6x + y=360$. Also, we can assume from the symmetry of the figure (if we consider the relationship between the angles) that the angles are arranged in a way that we can further analyze. Since the sum of the non - $y$ angles $x + 3x+2x=6x$, and we know that the sum of all angles around a point is $360^{\circ}$. We can also note that if we assume the angles are divided in a certain ratio. In this case, since the sum of the $x$ related angles is $6x$, and the sum of all angles around a point is $360^{\circ}$, we have $6x + y=360$. Another way is to assume that the angles are part of a regular division of the $360^{\circ}$ around the point. Let's first solve for $x$ from the fact that $x+3x + 2x=6x$ and the sum of all angles around a point is $360^{\circ}$. So $6x= 216$ (by considering the non - $y$ part), then $x = 36$.

Step3: Solve for $y$

Substitute $x = 36$ into $6x + y=360$. We get $6\times36+y=360$. Then $216 + y=360$, and $y=360 - 216=72$.

Answer:

$x = 36$, $y = 72$